Chelsea lost their Champions League opener 3-1, with Palmer scoring the visitors' goal.
"I feel like we deserved more, to be honest," Palmer said afterwards.
"We started well and I think we had early chances to score, but when you make mistakes at the highest level, then it’s hard to come back into the game.
"There was a bit of a lack of concentration and not managing the moments correctly, but I feel like we showed we can play against one of the best teams in the competition. I think we deserved more."
Palmer also said, "The manager said to us before that he knows we can go toe-to-toe with anyone, and I think we showed that tonight despite the result.
"It’s a good learning curve for tonight and to be back in the competition is nice so we just need to kick off from here.
"We’re not in this competition for it to be a learning curve. I feel like we showed tonight that we can compete and we want to do as best as we can."