The Mercedes driver finished second in Sunday's race, having lined up seventh after a DRS failure on his final Q3 lap scuppered his chances of matching team-mate George Russell's pole time.
Russell finished third, with Max Verstappen taking victory despite having started down in 10th.
But seven-time F1 world champion Hamilton says, though the cooler conditions on Sunday helped the team secure its second consecutive double podium, he could have taken victory were it not for his struggles on Saturday.
Speaking after the race, he said: "I definitely think being a little bit cooler, it seemed to work a little bit better for us. I can't tell you exactly why, but grateful for it.
"I was hoping it was gonna rain at the end so I could challenge Max, but we ran out of laps.
"So a bit of a better qualifying if the DRS was OK yesterday, we would have been in the run for the win.
"But either way, two seconds in a row, I'm really, really happy. So huge thank you to the fans for all the amazing support."
Hamilton now sits sixth in the drivers' standings, just 10 points shy of Carlos Sainz, while Mercedes is only 30 points behind Ferrari.
He says he doesn't know where the team's speed came from on Sunday, but added: "I was definitely struggling at the beginning of the race and wasn't sure whether I'd be able to catch the guys up.
"But, bit by bit, I got a bit more comfortable with the balance, had a really good start as well.
"I really want to acknowledge my team who have continued to push, never give up through this tough year that we've had so far.
"For us to be on the podium, both cars to be on the podium twice is pretty special for us. And really unlucky for George today. The other guys still have a bit of an edge.
"But we're clearly closing the gap. And this is just an amazing way to go into the break knowing that we have this performance.
"Hopefully, we'll bring some more into the second part of the season and start fighting with the guys up front."
