"I should have had five or six," he told the BBC after becoming the first player to score four in the first half of a Premier League game.
"When I missed the first chance I was upset but with the way they played and their high line I felt we'd get more chances," he said.
Palmer hit the post and had a goal ruled out for offside in a frantic first half where he shone. He also missed an open goal in the second half and hid his face in frustration.
"The manager set up a good game plan, we knew how to attack them with first-time passes in behind," said Palmer, as self-effacing off the pitch as he is dominant on it.
"Three points is what we needed and that is what we got," he said.
Palmer has proved Chelsea's star signing since he joined for 42.5 million pounds from Manchester City as the transfer window closed at the start of last season. Champions City could not promise him he would play every week.
Chelsea's American owners led by Todd Boehly and Clearlake Capital, who have spent more than a billion pounds on players, but failed to get results since taking over in 2022, must now believe he is worth every penny and Pep Guardiola may be regretting the decision to let him go.
He scored his 10th penalty on Saturday from 10 attempts since moving south, earning the 'ice-Cole' sobriquet.
Palmer has also earned an England place since joining Chelsea and has scored six goals so far this season for his club after doubters suggested he would run out of steam after his impressive start last season.
Coach Enzo Maresca who worked at City under Pep Guardiola, has been treating him carefully, keeping him fresh for the Premier League by leaving him out of the squad for the Europa Conference League.
"I knew Cole from years ago at City, he is a top player and just has to continue in the same way," Maresca said.
For Palmer, his role is simple. "I try and play every game the best I can."