The Me 262 was the 3rd Reich's first operational jet fighter. Although it scared the bejezus out of many Allied pilots, it wasn't as effective a weapon as it could have been, for several reasons:
It was deployed late in the game (July 1944). This was after D-Day and Stalingrad, when Germany was already on the back foot.
Due to Allied strategic bombing, production was slow and laborious. Secret manufacturing installations had to be built in forest clearings, sometimes literally underground.
Hitler was obsessed with the idea of utilizing the Me 262 as a fighter-bomber to continue the Luftwaffe's terror campaign against England. However, what the Reich really needed was a short-range interceptor to repel Allied bombing attacks. Hitler's meddling with production, design, and deployment resulted in the 262 being utilized sub-optimally.
Me 262 was indeed a rude shock for Allied pilots initially, as its great speed made it potentially extremely dangerous opponent: a skilled pilot could in theory always choose when to engage and when to flee.
However, in practice its impact was limited by low production figures, lack of fuel supplies for flying and particularly for training (which meant that the average quality of German pilots in general tended to diminish towards the end of the war), and by better Allied tactics. The limitations of the early jet engine meant that Me 262 was extremely unresponsive when landing in particular: it simply could not accelerate out of trouble if it was caught when attempting to land, and was more or less a sitting duck. Even though the Germans protected their airfields with extremely dense concentrations of anti-aircraft guns, many Me 262s were still shot down when vulnerable in this manner. In general, it was far too little far too late to make much of an impact to the overall war; and once the Allied air forces began to target German synthetic oil plants in late 1944 and thus cut off the remaining supply of fuel, it was basically game over for Luftwaffe anyway.
What's contested is how much Hitler's desires for a fast bomber had effect on Me 262's deployment. I've studied the subject of jet engine development at some length and tend to conclude with more modern studies that argue the real bottleneck was in engine development. Reliable engines were simply not available in quantity much earlier, and this situation was impossible to correct in 1943 - it would have required at minimum a much more concentrated research effort from 1930s, and even then it's doubtful whether reliable engines would have been available much sooner.
Hitler gets the blame largely because he's a) dead and b) Hitler; not a few Germans had incentive to blame him for just about anything. Boyne, for example, argues that the real culprit was Goering's 1940 decision to end development of jet engines as they wouldn't be ready until the war was thought to be over; given the problems the Brits had with their arguably simpler jet engines, I think even Goering's decision had limited effect. Perhaps more reliable jet engines might have been made available in quantity some six months earlier, but probably not much more than that.
Sources:
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Boyne, W. J. (2008). Goering’ s Big Bungle. Air Force Magazine, (November), 58–61.
Giffard, H. S. (2011). The Development and Production of Turbojet Aero-Engines in Britain, Germany and the United States, 1936-1945. PhD thesis, Imperial College, University of London.
Gunston, B. (2006). The Development of Jet and Turbine Aero Engines (4th ed.). Sparkford: Haynes Publishing.
Kay, A. L. (2002). German Jet Engine and Gas Turbine Development 1930-1945. Ramsbury: The Crowood Press.
Meher-Homji, C. B. (1997). Anselm Franz and the Jumo 004. Mechanical Engineering, 119(9), 88–92. Retrieved from http://dialnet.unirioja.es/servlet/articulo?codigo=430680
Meher-Homji, C. B. (1997). The Development of the Junkers Jumo 004B—The World’s First Production Turbojet. Journal of Engineering for Gas Turbines and Power, 119(4), 783. doi:10.1115/1.2817055
Schlaifer, R., & Heron, S. D. (1950). Development of aircraft engines. Boston, MA: Harvard University Press.
Staff of Power Jets (1945). Power Jets Report No. R.1089: The Jumo 004 Jet Engine.