Can we classify the Holocaust as one of Hitler's war time strategic mistake?
The German and Austrian Jewish population was about 750,000, of which three quarters were exterminated. Whereas the total German population was about 70 million. But 1941, when the extermination program began the number of Jewish forced labourers in German was 60,000, compared to the 2,000,000 foreign labourers (Fremdarbeiter) [source]. The Nazis decided that this was not an economic impediment to the Holocaust. Furthermore, in regions where the sudden absence of Jewish Labour would have been a problem they delayed the process to allow for their replacement.
It seems logical that the movement from forced labour to Extermination through Labour and the Holocaust of the Jewish population would have lead to costs (from the inefficiency of moving skilled workers to hard labour, to the expenses of diverting effort to commit to commit these awful crimes). These must have been the disruptions the Nazis had in mind and saw as no economic reason not to proceed. I will say the Jews brought from conquered lands for forced labour probably would have been an overall benefit to the German war effort, but I'm not including that as the "holocaust" as I'm assuming the alternative the questioner has in mind is assigning these foreign Jews to the Fremdarbeiter system anyway.
So no, it wasn't a massive strategic mistake. I've not considered other angles, like it's effect on their nuclear program, but in raw economic terms the Nazi's don't seem to have been punished for their terrible crimes. So, to conclude, Holocaust, whilst being one of the most horrendous crimes against humanity in history, wasn't as economically significant as OP may have suspected.
If the thrust of the question is, did Hitler lose World War II because of the way he treated the Jews and other people he didn't like, that is a very interesting question.
There are actually TWO issues here. 1) Did the cost of resources expended in the Holocaust help defeat the war effort, and 2) Did the "opportunity cost" of the Holocaust help the defeat the war effort.
The answer to 1) is probably not. Others have answered better than yours truly, that when you net out Germany's gains from "forced labor" and the cost of running the "program," the net result was probably close to zero.
The more interesting question is, did Hitler miss an opportunity to win World War II by treating the Jews (and others) BETTER than he did?
One of the big "what ifs" of World War II, was "Suppose Hitler had declared war on "Russia" instead of the Soviet Union, and posed as a "liberator" to the people of the Baltic, Belarus, Ukraine, etc., enlisting their young men in his army (and depriving Russia of them). What would have happened?"
In fact, many "Soviet" people initially welcomed the Germans as such, until the effect of Nazi policies became apparent. Without going into the question of whether Hitler would have actually won the war, it is safe to say that he would have gotten "closer" to winning if he had treated Jews, Poles, and non-Russian Soviets better. (Fewer partisan attacks in Russia and revolts in Warsaw, for one.) Not doing so was a major strategic mistake.
Regarding what he considered a "lost opportunity," a former Luftwaffe pilot (aged 77 when I met him in 1991) opined, "If we had hung on to people like Einstein (the Jewish atomic scientists), they could have won the war for us. I don't love those people, but I don't hate them, either." He was perhaps a minority among Germans is thinking in terms of "whatever we needed to do to win," but considering who he had been, that was a very interesting observation.
DISCLAIMER - the answer is written from the point of view of Reich's rulers
Invading the USSR was not a strategic blunder, the timing however was unfortunate.
The alliance with Japan was intended to provide the Soviets with a second front in the east, drawing their troops away from the west, thus making things easier for the Germans. And for a while it worked, until Stalin finally gave permission to withdraw some troops from Siberia to reinforce Stalingrad in light of Japan not launching its campaign as expected.
The elimination of Jews was popular at home, made for good propaganda. The resource drain on German manpower and industry was relatively light in comparison. The system also provided for a nice base of cheap (slave) labour, most Jews were NOT as is often portrayed gassed or shot to death, they were worked to death (the gas chambers in the larger camps were used mainly to dispose of the sick and weak, the rest were sent to factories in the vicinity where they were rented out to the factory owners, the SS being paid for their service).
This system was put in place in part as a response to the initial and largely independent killings undertook by invididual Wermacht and SS units in eastern Europe, which were starting to eat up valuable supplies of bullets and manpower needed on the front lines.
In Hitler's ideology exterminating Jews was the purpose and the goal of the war.
The large-scale extermination started in 1942 when Germany's victory became uncertain. At that time Hitler had no longer possibility to postpone the extermination until the victory.