The allies had their own AA guns that were almost or equally capable.

The British (and the Commonwealth) had their QF 3.7" (94mm) AA gun, that had properties close to the Germans' 88mm guns. They also had about 500 ww1 3" AA guns in 1939 that soldiered on as heavy AA guns until replaced by more modern 3.7" guns.

The French used both older AA guns derived from their famous 75mm mle1897 field gun (essentially the gun mounted on an AA mounting and with new sights and ammunitions) and a more modern design that came out in 1928.

The Americans used both the older 3" M3 AA gun based on a M1898 coastal defence gun, but with modern sights, ammunition and carriage (the one for the Bofors 40m gun) and when available their more modern 90mm M1. By the time the US entered ww2, most frontline forces had switched over to the 90mm, while the 3" soldiered on in garrison, training and home front duties.

As you can see, the Allies had their own powerful AA guns. The question might then be, why did they not use them as the Germans did?

Well, they did, to some extent. The British used 3.7" AA guns to knock out Italian bunkers at Tobruk when they conquered it in January 1941.

However, early war the Germans often had local air superiority, and heavy AA guns were in short supply and thus reserved to protect strategically important sites and targets from German (and Italian( air raids.

Later in the war, the Allies had much better anti-tank capabilities, with 6pdr/57mm M1 AT guns, bazookas, PIATs, 17pdr AT guns, plenty of anti-tank mines and so on. They did not have the same need to press AA guns unto service as anti-tank weapons. That said, the Americans did use their 90mm gun in their M36 tank destroyer.

The Germans mostly used their 88mm guns as anti-tank weapons early war, when Allied and Soviet heavy tanks proved too tough for their 37mm anti-tank guns - using an AA gun as anti-tank weapon is dangerous, as it has a high profile and is hard to dig down quickly, making it vurnurable to enemy fire.