The Togo international joined City from Arsenal in 2009 but failed to make an impact at the Etihad Stadium before he was sold to Spurs last summer.
"It's going to be important for me to prove how good I am, but I don't have any pressure that says I have to beat Man City because of the way they treated me, because they bought me expensively and sold me for cheap," Adebayor told Goal.com. "That has nothing to do with football.
"I just have to go out there and play my football and find a way to help Tottenham win the game because now I play for Tottenham."
Tottenham welcome Manchester City to White Hart Lane in the Premier League on Sunday.