Milan secured a late victory when defender Matteo Gabbia eluded his marker and found the top corner with a perfectly timed header from a free kick.
The win marked Milan's first victory in the Derby della Madonnina since 2022 after suffering six consecutive defeats to Inter.
"It was an important match. First of all, because it’s a derby that Milan hadn't won in a long time. It was important given the moment we were going through," Fonseca told DAZN.
"I think the players showed a lot of courage and we deserved the win. I don’t remember seeing a team who caused this many problems for Inter in a long time."
Fonseca brushed off the suggestion that the victory had eased the pressure on him after a poor start to the campaign in which Milan won only once in five matches across all competitions before Sunday.
"It makes little difference to me because I don’t read or listen to these things," he said.
"It will be a week with a little more confidence, but the important thing for me is to continue seeing the players believe in our ideas, the way they have done so far.
"We know that we must improve, but this was a victory for the players today," Fonseca added.
Inter coach Simone Inzaghi acknowledged that Milan were the better team at the San Siro and questioned the attitude displayed by his players at times during the match.
"Of course, Milan are a very good team. They did better than us this evening and deserved the victory," Inzaghi said.
"We had the wrong approach and weren't enough of a team, which is rare for us. We didn't start either half with the right attitude."
With two draws and one loss in Serie A so far, defending champions Inter have endured a mixed start to the campaign.
"It's unexpected, we had worked well over the last couple of days in training, but the approach was wrong in both halves. Now we’ve already dropped a few too many points in Serie A and this is particularly sore," Inzaghi added.
Milan next host Lecce in Serie A on Friday while Inter will travel to Udinese on Saturday.