Tuchel made signing an elite striker his top priority this summer after his side frequently misfired last term, despite their Champions League success.
Midfielder Jorginho was the club’s highest Premier League scorer, although all seven of his goals were penalties.
Tuchel has conceded that he should shoulder some of the blame for the highly rated Abraham’s departure.
“He did some good preparation matches, he was clearly not happy with the last half a year and maybe he has reason not to be,” Tuchel said after a 2-2 pre-season draw with Tottenham.
“Maybe it was also my fault not to push him or trust him, I can absolutely understand that he wants more minutes.”
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