Leclerc, who crashed out heavily at the end of the second lap, told reporters the pair had raced too hard on the opening lap after sharing the second row of the grid, with Hamilton forced off into the gravel and dropping from fourth to 10th.
The seven-time Formula 1 world champion ended up sixth and is now 76 points behind Mercedes' championship leader and race winner Kimi Antonelli, who at least gave Italy something to cheer on a day when Ferrari let them down.
"We're just not executing as well as we can. Not as well as the other teams are. But we were at other points in the season," Hamilton told reporters.
"I think it comes down to rules of engagement. When I was at Mercedes, we had written rules of engagement. And we never really had it too bad.
"There was a moment maybe with me and Nico (Rosberg) a couple of times. But more often than not it was good. Here there are no rules. And I think that's something that needs to probably change."
Hamilton joined Ferrari from Mercedes last season, when the team failed to win a race. He and Leclerc have both won in 2026 already, and Ferrari are second overall to Mercedes.
The Briton, who came into the race third overall and level on points with Mercedes' second-placed George Russell, said he felt "massively gutted" for the loyal fans, with Formula One reporting a record crowd for the weekend of 403,666.
"I think today we just lost so much ground to them (Mercedes) on points, and it's far too late for those decisions to come," said Hamilton, who also dismissed Leclerc's explanation to reporters about the incident that "we went too far, I think".
"I was ahead into Turn Two. By the apex I was ahead, so there's no 'we' in it," said Hamilton, who had complained at the time that "Charles pushed me off".
Rosberg, the 2016 champion now a pundit with Sky Sports television, backed Hamilton.
"It’s very straightforward and simple. Lewis was ahead going in, so Charles has to leave room," said the German. “And he didn’t, so it was 100% Charles’ fault, and that’s it.”