Arsene Wenger's side have won four on the spin since they lost 5-1 in the second leg of the Carling Cup semi-final at White Hart Lane last month.
Arsenal travel to Old Trafford for their FA Cup fifth-round clash against United at the weekend and midfielder Hleb is certain victory there will ensure the Spurs defeat becomes a distant memory.
Alex Hleb said: "It was very important for us to get things right again after the Spurs defeat.
"Sometimes matches like that one happen in football - maybe we didn't have the right level of concentration, it's difficult to say.
"It seemed to me that they maybe wanted the win more than we did. But then, it was as if every shot they took went in."
Full-back Gael Clichy also felt the performances have atoned for the defeat to their rivals.
He added: "I think it was really important to do that, for the fans and the club.
"So we have to carry on like this - combining that spirit with the kind of game we play, then we can achieve great things this season."
Central to their hopes of silverware is Adebayor, the Togo international striker who has scored in his last nine games for his club.
"He's in fantastic form. It's great for him and great for the team," Hleb added.
"Now with important games such as Manchester United and AC Milan and others coming up, it's ideal to have a striker who is taking his chances whichever way they come and showing such all-round ability.
"Everything is coming off for him at the moment."