Hmm, I suppose, a "mistake" in a technical sense is defined in terms of mini-max position evaluation, assuming infinite computing power:

eval(position) = -1 (loss), 0 (tie), or +1(win)
IsFatalMistake(move) = (eval(position before the move) > eval(position after the move) AND eval(position after the move) == -1)

With this definition, either giving away the pawn or missing the checkmate (or both) wasn't a fatal mistake, since the game was already lost before the move :)