City have toiled at home and abroad over recent weeks, with defensive errors proving costly.
The reigning Premier League champions were once again undone by a set-piece against Spurs, as Steven Caulker opened the scoring, but hit back through Sergio Aguero and substitute Edin Dzeko to claim a morale-boosting success.
Mancini concedes that his side were far from faultless on Sunday, while Gael Clichy picked up a knock that will require attention, but the Italian feels things are heading in the right direction.
He told Sky Sports: "Tottenham are a strong team that are very dangerous away.
"The two problems are that we conceded again from a set-piece and the other problems is Clichy with his back. Apart from that we were fantastic.
"We need to have more concentration on set-pieces. But the players were fantastic and I can see that they showed the same spirit we had last year.
"I also want to say thank you to all of our supporters because they have been very close to us for the past two weeks and I want to say thank you."