The decision to stick to gasoline engines was a consequence of Germany's hasty rearmament and chronic bureaucratic inefficiency. Gasoline engines were initially the logical choice for the German panzer arm because such engines were both cheaper and easier for German industry to produce. Among the designers at the German army procurement office (Heereswaffenamt) the dominant thought was that the range penalties of gasoline would not hinder operations. Few military planners outside of armor specialists like Guderian foresaw the scale of armored operations and the free-ranging distances that they would cover. Fall Gelb illustrated the shortcomings of Germany's poor logistical tail and the limited range of the panzers. Several times in the French campaign the panzers had to be airdropped fuel to continue operations. Barbarossa made the range problem even more apparent. Despite this, the Heereswaffenamt still favored a conservative approach to tank design. The Tiger was born in this mentality as a breakthrough tank (a design that first started kicking around in 1937) in which performance was more important than fuel economy.

Hitler, for all his shortcomings, actually had some smart ideas on tank design and directed that the next generation of medium tanks to have diesel engines. German industry though was not up to the task of retooling production lines. Speer ignored Hitler's directives to expand diesel production as unnecessarily disruptive to existing German industry. The Daimler Benz design (VK 3002[DB]) for what became the Panther had a diesel engine and was heavily influenced by the T-34. However, the conservative Heereswaffenamt opted for the gasoline-powered MAN design and informed Hitler that the Daimler Benz design could not be produced in the numbers the Germans needed.

Sources

Forczyk, Robert. Tank Warfare on the Eastern Front: 1941-1942 ; Schwerpunkt. Barnsley: Pen et Sword Military, 2014.

Green, Michael, and Gladys Green. Panther: Germany's Quest for Combat Dominance. Oxford: Osprey, 2012.

Zaloga, Steve, and Howard Gerrard. Panther Vs. Sherman Battle of the Bulge, 1944. Oxford: Osprey Pub, 2008.

As a rider to this question, what was the thinking that influenced the Soviets to switch almost universally to diesel for their armor so early compared to everybody else?

For all the criticism of German logistics in this thread, in the interests of fairness its worth referring to the efficiency of German refuelling logistics (at least compared to the Western Allies).

The German used fuel cans (Jerry cans) which were of very sturdy construction. This meant that any number of vehicles could be refuelled simultaneously, and being able to withstand anything but a direct hit, losses were kept to a minimum and a half full jerry can could be strapped to the outside of vehicle for later use.

The French used a bowser system, which had a limited number of fuel lines per bowser. French vehicles therefore had to queue to be refuelled which was a colossal waste of time of effort and always carried the risk that only a proportion of vehicles could be refuelled in the time available.

The British did use fuel cans but these were of extremely flimsy construction. So flimsy indeed, that it wasn't uncommon for the cans to rupture on the back of a lorry during a hard drive over broken terrain. What's more, half filled cans simply had to be discarded as they simply couldn't be carried around leaking petrol everywhere.

When you consider the effort involved in supplying fuel to the front line, the advantage conferred by the jerry can over the British cans was quite considerable.

Follow up question:

Would having diesel technology tanks have made much of a difference to German tank warfare? Hard to quantify but are there any theories?

Ok another follow-up: Why are the Americans still using petrol engines? (or atleast Jet Engines which can pretty much run on anything) Is this just because it runs faster than diesel or are the Americans not interested in Diesel engines at all?

Why exactly would diesel be preferred?