The Togo international returned after nine weeks out through injury, illness and family issues to come on as a second-half substitute in last weekend’s 2-1 win over Sunderland.
Adebayor’s return to action proved unpopular with some sections of the Spurs support, however, who jeered his introduction.
He was met with a similar response by some sections of the White Hart Lane crowd when he was substituted in Wednesday???s 1-0 win over Sheffield United in the first leg of their Capital One Cup semi-final.
But Pochettino feels the booing can adversely affect the players and urged them to get behind Adebayor and the team when they take on Leicester in the fourth round of the FA Cup on Saturday.
“I think this is best because all players need to feel the support from the stands from our supporters,” he said.
“I think it’s better for him and for the team. We always need to create a great atmosphere to try to get success.”
As well as the Premier League, FA Cup and Capital One Cup, Tottenham are still involved in the Europa League and Pochettino knows their stamina will be tested in the weeks ahead.
“We need to keep fighting in the four competitions,” he added. “You can see that we have ahead a very busy period, a lot of games.
“Tomorrow (Saturday) will be the 37th official game, that’s nearly one season, and so we need to keep all of our players in a good condition to fight in the four competitions.”