In addition to /u/Meesus's insights, the casualty comparison you're making is skewed. The Axis casualties, especially those during the Operation Uranus encirclement were largely irrecoverable: killed, captured, missing, or wounded too severely to ever return service. At most 25,000 of the wounded were evacuated, and possibly lower; the majority were left to be taken prisoner. There are still debates over exactly how many irrecoverable casualties the Germans, Romanians, Hungarians, and Italians took during the battle as a whole. However, the numbers tend to oscillate around 400,000 irrecoverable from what I have seen. I have seen some numbers as high as 600,000 if you include all combat up to 2 February 1943, but I cannot speak to the veracity of these.^(1) Meanwhile, of those 1.13 million Soviet casaulties, approximately 479,000 were irrecoverable; many of the sick and wounded would return to service, unlike the sick and wounded of the encircled Wehrmacht forces. This is, then, a much less lopsided casualty ratio.

As /u/Meesus correctly points out, war is about far more than just casualty ratios. The Soviet victory at Stalingrad dislocated the southeast 'hump' of the Wehrmacht's front line and rather abruptly put the Wehrmacht on the back foot, after it had spent the summer driving forward at an aggressive clip in Operation Blau. In conjunction with successive operations like Little Saturn, Star, and Gallop the Soviets spent the winter of 1942-43 rolling back a lot of the Wehrmacht's gains from Operation Blau. See Map 12 from Glantz & House, When Titans Clashed. This string of offensives was made possible by the Soviet victory at Stalingrad, which dislodged the Germans from their positions in the southeast and in the process inflicted casualties to the Germans and their allies from which they could not quickly recover. Indeed, after the mauling of Italian 8th Army in Little Saturn, the Italian involvement in the Eastern Front was at end. This heady success was, of course, temporarily dashed by Manstein's 'backhand blow' at Khar'kov and the Donets Basin in February-March 1943. However, Stalingrad marked the high-water mark for the Axis advance into the Soviet Union. From the Soviet Uranus offensive onwards, the Red Army was able to contest - and eventually claim decisively - the strategic initiative, while the Wehrmacht found itself confined to contesting the operational and tactical initiative at individual points in time such as Khar'kov. The Axis casualties incurred at Stalingrad and then during the Red Army's winter offensive could not be immediately replaced. Indeed, the evaporation of 6th Army, parts of 4th Panzer Army, and the Axis-allied armies made the Wehrmacht's position untenable and created the conditions for the Red Army's advance. In this sense, it is not hard to see why Hitler wasn't popping the champagne bottles for the Battle of Stalingrad.

1. This is from the conclusion of Stephen Walsh's Stalingrad: The Infernal Cauldron, and like many of Walsh's assertions in this book there is no footnote or clarification to be had. I do not know how he arrived at this number, nor what the breakdown of KIA, MIA, POW, and WIA is. With that said, Walsh was a Soviet studies lecturer at the Royal Military Academy Sandhurst, and RMA Sandhurst is generally well-regarded for Soviet military studies. In any case, the 330-400K irrecoverable range is more easily supportable; see e.g. Glantz & House, When Titans Clashed, Mawdsley, Thunder in the East, these handy digitized Wehrmacht casualty records, and Richard Evans' The Third Reich at War.
2. My general thesis here is built on the academic consensus surrounding Stalingrad's importance. For further reading, I would recommend

• Glantz and House, When Titans Clashed (2015 edition)
• Glantz and House's Stalingrad trilogy
• Mawdsley, Thunder in the East
• Citino, Death of the Wehrmacht
• Bellamy, Absolute War
• Erickson, The Road to Stalingrad and The Road to Berlin
• Glantz, After Stalingrad: The Red Army's Winter Offensive 1942-1943

There's much more to warfighting than casualty counts. The Soviets suffered serious losses during the Fall Blau campaign and ensuing battle for Stalingrad, but, despite the significant gains the Axis forces made in 1942, they failed to completely shatter the Soviets. The centerpiece of their forces in the region - the 6th Army - was bogged down in the fighting for Stalingrad, and their flanks were left overextended and undersupplied.

The Soviet counteroffensive, on the other hand, completely upset the Axis lines. The Romanian 3rd and 4th Armies on the flanks of the 6th Army in Stalingrad were shattered and the 6th Army was famously encircled and besieged. The German army, already worn down from the months of fighting in Stalingrad, was unable to launch a successful counteroffensive to break the encirclement on the 6th Army, and it would be faced with a collapse of the front entirely as the Soviets launched the second stage of their counteroffensive, culminating in the collapse of the Hungarian 2nd and Italian 8th Armies in the north and bottling up of the German 17th and remnants of the Romanian 4th Armies on a bridgehead south of the Sea of Azov. The collapse of the front was ultimately stymied and fortunes slightly reversed in what became the 3rd Battle of Kharkov, but the front that stabilized left German forces in the north near Rzhev exposed enough that they'd have to withdraw as well, eliminating the threat to Moscow that had stood since the previous winter.

Critically, unlike the Fall Blau offensive, which inflicted major losses on the Soviets and threatened - but ultimately failed - to unhinge the entire front, the Soviet Operations Uranus and Little Saturn destroyed the most powerful German army in the region, bottled up a second army on a bridgehead where it was unable to contribute meaningfully to the fighting, forced a withdrawal of German forces near Moscow, and removed the not-insignificant forces of the Italians and Hungarians as effective fighting forces from the Eastern Front. German losses in equipment and experienced personnel - especially in terms of air crews - were something they would never be able to recover from.