The result gives City the advantage heading into next week's return leg at the Etihad Stadium, where Mancini's charges will now be favourites to progress to the round-of-16.
Sergio Aguero came off the bench to score the winner six minutes from time after an Alvaro Pereira own goal had cancelled out a Silvestre Varela strike.
Mancini said: "I think it was a good result because it is difficult to win here.
"I think we won this game because we played very well and didn't give more chances to score to them.
"I think the guys were fantastic."
Mancini was generally pleased with the performance of Mario Balotelli, who had been playing his first game since serving a four-match domestic suspension for stamping on Tottenham's Scott Parker.
The City boss had spoken before the game of the importance of Balotelli remaining focused on the game ahead of a crucial period for the team.
He said: "I think Mario did very well, he played very well. He was calm and it is important he continues like this.
"I think this [provocation] can happen every game.
"For this reason I spoke with Mario before the game.
"I said, 'Mario think and play, think what you should do during the game. Forget other things.' I think only this is important."
Yaya Toure also had an influential role on his City return after missing eight games due to the African Nations Cup.
Mancini said: "I think Yaya is an important player for us but Yaya can't win alone. He needs all the other players.
"I think this evening [Thursday] all the team played well because, if not, it is impossible to win here.
"I don't know how many Porto have lost on this pitch. I think if you win here you should play well with all the team. If not, it is impossible."
Porto, last season's Europa League winners, went into the game boasting a formidable record.
The Portuguese champions have lost just one league game this season and had not been beaten at home in a major competition.
Mancini said: "I think we are 60% to go to the next stage but we know we play always against Porto.
"Porto is a top team, a top squad.
"It will also be a difficult game in Manchester. We should keep the same concentration we had tonight [Thursday]."
Porto coach Vitor Pereira said: "We scored a good goal but in the second half City started better and scored their equaliser.
"They created a lot of difficulties for us.
"They played very well on the counter-attack and scored the second goal."