Inter won thanks to two own goals, but Mourinho insisted afterwards: "In the first half, when both teams had 11 men on the pitch, we played very well.
"We went behind, but the team reacted well and scored a good goal with Quaresma. Catania played their game, although the right result would have been 3-1, 4-1 or 5-1 to us."
The win temporarily puts Inter on top of the Serie A table with four points from two games.
"I had thought to introduce more attacking players like Amantino Mancini and Adriano in the second half, but with the red card that was not possible.
"These are three important points for us, especially as Maicon had a great game despite only returning from Brazil yesterday and I didn't think Patrick Vieira could handle more than an hour."
Mourinho remained unflappable on the touchline even when a scuffle broke out at the half-time whistle.
"I was not tense, not even in the first half. I try to be relaxed when I'm on the bench. Sometimes you need to communicate with the players, but my experience tells me when we have the opportunity to score and don't take it, we run a big risk."