Inter, who had Sulley Muntari sent off before half-time, came back from a goal down to salvage an unconvincing victory.
"In the first half, when both teams had 11 men on the pitch, we played very well," the Portuguese said after the game.
"We went behind, but the team reacted well and scored a good goal. Catania played their game, although the right result would have been 3-1, 4-1 or 5-1 to us.
"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 will make his Champions League debut with Inter when they visit Greece's Panathinaikos on Tuesday.
Child
In the wake of the victory, Muntari slammed Catania's Giacomo Tedesco for making the most of the challenge which saw the Ghanaian sent off at San Siro.
"The referee saw that I lifted my arm and he’s right in that I should not do that, but I was just protecting the ball," said Muntari.
"Having said that, not even a child would’ve fallen in such a dramatic fashion. He went to ground as if struck by Mohammed Ali!"