The Blues faced a tough test at Stamford Bridge against a Brentford side that began the day fifth in the Premier League.
Chelsea broke the deadlock midway through the first half when Joao Pedro reacted swiftly to a rebound, firing in the opener. Both teams had chances to score again, but the game was sealed in the 76th minute with Palmer converting a penalty to secure the victory.
“So he was ill; it's running through the squad. There were a couple of players playing today who were complaining about their chests, but they put in a magnificent effort,” he said.
“I felt that's why we weren't good with the ball. I won't give you names – it's not right for me to do that – but it's why I'm so happy with the attitude of the group to get through this game.”