Thiago Motta, Diego Milito, Maicon and Dejan Stankovic netted for the champions in their second Serie A outing of the season, with Gennaro Gattuso being sent off in the first half for their demoralised derby rivals.
"It is hard to better the result but yes we can play better," he told a news conference after the 'home' Milan fans at a packed San Siro went home in near silence.
"Today was fantastic at every level but I still have some question marks which is why we are a top team."
The performance was a marked improvement on last weekend's 1-1 home draw with promoted Bari with new signings Milito and Samuel Eto'o linking up well and Dutch debutant Wesley Sneijder contributing as playmaker.
"Lets go forward with a balanced view, I didn't cry after the Bari game and I won't go mad now. When we win I stay with my feet on the ground," Mourinho said, agreeing it was a risk to give Sneijder a debut a day after he joined from Real Madrid.
"He is a great player, physically strong. As we won, Mourinho is great, if we lost Mourinho was stupid."
Rookie Milan boss Leonardo, whose side looked bright in last weekend's 2-1 win at Siena, kept a level head like Mourinho and refused to blame any of his players for the defeat.
Inter scored their first three in the last 16 minutes of the first half during which time an injured Gattuso was sent off having earlier asked to be substituted, only to stay on the field because Clarence Seedorf was not ready.
"I think the first half hour we did OK, we were equal, we had some chances. In my opinion we were better than Inter at the start but the first goal changed things," the Brazilian said.
"There was five minutes where lots happened and it was key to the match. We can't come up with a definition of where we are. We've played two matches and done lots of things positively."
Milan have been frugal in the transfer market despite selling Kaka to Real Madrid but Leonardo ruled out more buys.
A Milan spokesman said Gattuso had suffered an ankle injury and could be out for two weeks, which would make him unavailable for Italy's upcoming World Cup qualifiers.
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