City cruised into the last 16 as they ran out 4-0 winners at the Etihad Stadium to complete a 6-1 aggregate success over the holders and Portuguese champions. Yet after taking the lead through Sergio Aguero after just 18 seconds, City had to wait until the 76th minute to double their advantage after spurning a number of chances.
Mancini said: "It is not easy to beat Porto, they are one of the top teams in Europe and I am happy that we are going to the next stage."
He added: "It was a good night but it was not easy. We had other chances to score but we didn't score, and when you don't score, you can have other problems."
City's second came from substitute Edin Dzeko before the sending off of Rolando preceded further strikes from David Silva and David Pizarro in the closing minutes.
Porto coach Vitor Pereira felt the scoreline flattered City and his team, who scored the first goal in the tie last week, were unlucky.
Pereira said: "Up until the second Manchester City goal, Porto were the best team.
"We played much better but we know Manchester City have a good team and they used the counter-attack well.
"They have great players up front and the second goal caused us difficulties. We wanted to change the game but the sending off changed it in favour of Manchester City.
"The scoreline does not show what happened on the pitch."