The Togo international has scored only once in all competitions this term - the final goal in Spurs' 4-0 rout of QPR in August.
Adebayor managed 14 goals last season, having regained a place under Pochettino's predecessor Tim Sherwood after being frozen out under Andre Villas-Boas.
Although he has only found the net on one occasion this term, Pochettino is confident the former Arsenal man will come good.
"I believe in Adebayor," he explained.
"We know always a striker maybe has some period of difficulty to score but he has made a lot of effort for the team.
"The more important thing is we are convinced that he or another team-mate can arrive at the possibility to score. I am happy with his performance.
"He knows he needs to score because a striker always lives to score but I believe in him and have no problem."
Pochettino's side take on Group C rivals Besiktas in the UEFA Europa League on Thursday, looking to gain momentum after drawing their opening match against Partizan.
Kyle Walker is Tottenham's only definite absentee and Pochettino remains in the dark as to when the defender will return.
"At the moment it is impossible to give you the date. It is a good recovery at the moment," he continued.
"We are happy, but it's impossible to predict the time, when he is maybe ready to train with the team and to start to play."
