The seven-times Formula 1 champion qualified fifth, with teammate Charles Leclerc fourth, but will drop to 10th after a penalty carried over from last weekend's race at Zandvoort is applied.
Despite that blow, the Briton saw plenty to be positive about only a week after he and Leclerc crashed out at the Dutch Grand Prix and barely a month since he described his performance as 'useless'.
"These last couple of races have been tough ... but we have let all that go and we are focused on delivering the job, and absorbing the positives and the passion of the fans," said the 40-year-old.
"Of course we are not where we want to be, but fourth and fifth is progress and I want to keep on working with my engineers to extract more."
Hamilton, a five-times winner at Monza, has yet to stand on the podium in 15 races since he joined Ferrari from Mercedes in January and has not won in more than a year other than a Saturday sprint.
Even while driving for Mercedes, Hamilton had plenty of Italian fans -- but, in red overalls and despite obvious setbacks in adapting to the car and team, he has been truly feeling the love of all things Ferrari.
"So far, it has been incredible, amazing. I don’t know what other word I can find for it," he said.
"Showing up at the factory on Wednesday and driving to Milan and seeing so many people and then coming into the weekend the tifosi are everywhere, they are hiding behind trees. There are so many of them.
"As you leave the track they are on both sides as far as you can go and it is incredible to see the love that people have for this team. There is nothing like it."