The seven-time world champion badly damaged his car when he crashed at the end of final free practice and, after a rapid rebuild, qualified sixth before an incident-hit race of collisions, penalties and near-misses.
The Briton, however, rejected the idea that he has been unlucky.
"No, not unlucky. But I do think about the mistake that I made yesterday.
"So, I take full responsibility for the fourth place I ended up getting because I damaged the car. And then, when they built the car, they missed something on the suspension. The balance was completely different, so I was a good couple of tenths, maybe three-tenths, slower than I should have been in qualifying.
"Then, in the race, I ended up further back with the incident and a five-second penalty, so it was just like a domino effect from a mistake from myself."
Hamilton collided with his former teammate George Russell of Mercedes on the opening lap and was given a five-second penalty.
When he served the penalty during his pit stop, he almost hit a mechanic as he left the pit.
The stewards launched a post-race investigation for an unsafe release by Ferrari.
"The green light went, so I went. That's more probably on the team ultimately than me. When it happened, I noticed him and then I stopped.
"My heart sank for a second, but I am so glad he is OK."
The mechanic was trying to make an adjustment to the wing setting on Hamilton’s car when the green light came on.
"The team have been doing a great job with strategy and pit stops," added Hamilton.
"We are continuing to improve the car and I think our pace today, without the damage, could have been enough to be challenging for the win.
"This weekend has been a bit unfortunate, like Silverstone again, but it is great to see the performance we are bringing to the track and how the car is improving.
"We have more stuff coming, in the pipeline, so it is encouraging. There’s a long way to go and I am going to step up in terms of focus levels for next week."
After finishing fourth behind Mercedes’ championship leader Kimi Antonelli, his Ferrari teammate Charles Leclerc and four-time champion Max Verstappen of Red Bull, Hamilton moved up to second in the drivers' title race, 45 points behind leader Antonelli.