Spurs went into Sunday's game at the Emirates Stadium confident of doing the double over their rivals for the first time in 19 years but they went down to a humiliating 5-2 loss after a stunning comeback from the Gunners.
But Adebayor has backed his team-mates to bounce back, and told Spurs TV Online: "If you want to be champions these games against the likes of Manchester United are the kind of games we have to be winning. The Arsenal game has been a tough one, the defeat is very heavy, but we have to carry on. "
He added: "We have to keep focused. We have to show character in front of our fans and manage to win that game."
The defeat put a severe dent in Spurs' title hopes - they trail leaders Manchester City by 10 points - and also increased Arsenal and Chelsea's hopes of catching Harry Redknapp's team, who sit third in the table.
After losing just once in their previous 15 games, last weekend's defeat, and the manner of it, came as a surprise for most. For Adebayor the reverse was particularly hard to take given that he has been the subject of hatred from Arsenal fans since leaving the club three years ago.
The striker, who wisely chose not to celebrate after scoring his goal, acknowledges that Arsenal deserved to win, however.
"After my penalty I thought game was over, but they showed good character, played some good football and came back so congratulations to Arsenal," the 28-year-old added.
"Unfortunately we didn't manage to beat them but the season is long, we just have to keep focused and keep going. After losing 5-2 to Arsenal we can't ask for a bigger challenge than playing Manchester United, but we are looking forward to it.
"It will be a tough game but I think we are ready for it. We just have to show personality and character and bounce back as quickly as possible."
Source: PA
Source: PA