Hamilton, starting 15th, got as high as second on a Monza circuit affected by rain and mist before an extra tire swap cost him. However, the McLaren driver finished in the points in seventh place, one back of Massa.
Hamilton goes into the last four races with a 78-77 advantage over Massa, who had started his Ferrari nine places higher than the Briton.
"I think we all missed a big opportunity today. I think Ferrari missed an opportunity with me being right at the back," said Hamilton, who has already won two races in the rain this season. "You know what I can do in the wet, so there was no doubt in my mind that I could do a good job today and I could catch up in the rain."
Hamilton said he stuck with the extreme wet tires after his first pit stop despite the showers easing because his team had forecast more rain.
"I showed I'm quickest in the wet and showed that I have great pace. I think the win was possible today considering the position we were in," he said.
"If we had chosen to be on the intermediate tire on the first stop ... we would have been further up." The steady rain didn't help Massa's title challenge even though he gained a point overall, but Hamilton may have even passed the Brazilian in the closing stages if his front tires hadn't overheated.
"The main thing is I finished ahead of Lewis," Massa said.
Both Massa and teammate Kimi Raikkonen experienced front-wheel problems that kept their cars from realizing their potential at their home race. Massa had also needed a late engine change.
"At least he gained one point on the leader of the championship," Ferrari team principal Stefan Domenicalli said of Massa. "But for sure, considering what was the situation this morning, he could have done better.
"But going back to the (weather conditions) of today, it could have been worse." Raikkonen, the defending F1 champion Raikkonen who started 14th, set the fastest lap but could only finish ninth and now trails Hamilton by 21 points.
With only four races remaining and Ferrari's once-sizable constructors' lead shrunk to only five points, Domenicalli wants his team's cars to be improved quickly.
"Unfortunately, there is a characteristic on the car that ... in certain window and in certain conditions we need the right temperature for the tires to work," he said. "It is true we don't like the rain and cold but we cannot do anything about that, so all we can do is work very hard and see what we can do to improve the situation."
In the meantime, Hamilton isn't sure the championship is his to lose.
"Perhaps maybe, but I'm not looking at it that way," Hamilton said. "Kimi is the world champion, so it's his championship to lose."
