Edin Dzeko headed his first goal since November 5 to sink their rock-bottom hosts as City bounced back the hard way from home defeats in the FA Cup and Carling Cup.
Blues boss Mancini said: “It was really important that we beat them after two defeats in the cups.
“It was a really important three points because it was a difficult game, though we had three or four incredible chances to score a second goal.
“But it was clear it would be difficult to the end. Anything can happen in that situation. We knew it would be difficult, and Roberto Martinez is a fantastic manager.
When you are only winning 1-0, it is normal to be nervous, every manager is nervous in this situation
Dzeko broke his barren spell with a brilliant 22nd-minute header just in time for the visit of title rivals Tottenham - where the Bosnian ace rattled in four goals back in August.
Mancini said: “I’m very happy for Dzeko. He deserved to score a goal, and it was an important one for us. Now I hope he can go on and score more.
“Tottenham are having a fantastic season - they are a very good team, and it will be a fantastic game on Sunday.”
David Silva is back but City will still be without suspended skipper Vincent Kompany and African player of the year Yaya Toure when Harry Redknapp’s men come calling.
Mancini said: “You want every player available for every game, but the players who played gave everything tonight. Maybe we didn’t play well but the important thing is we won.
“We have injuries and players away, but the squad is doing everything to win every game.”
