Patrick Cutrone scored his eighth goal of the season in the 14th minute of extra time to hand Gattuso his third win in seven games as Milan boss.
It has been a tough start to his reign at the San Siro and Gattuso made reference to his previous poor results, but the former midfielder called on his team to reproduce their level of performance against Inter in future matches.
‘Perhaps I am the worst coach in Serie A but I always want to win, even playing in the garden with my son,’ he told Rai Sport.
‘I want my lads to prove that what I saw tonight was not a fluke, then we’ll take it one game at a time.
‘Now there are two difficult games coming up in Serie A and we need points to climb the table. I didn’t see much difference between this performance and the defeat to Atalanta. Some might call me crazy for saying that. We had the game with Verona in hand too until we conceded the first goal like dummies.
‘This is a team that does well until it runs into the first hurdle and today we overcame the hurdles.’
Milan visit Fiorentina in Serie A on Saturday when Gattuso will be hoping to see his side climb from their current position of 11th in the table.