Palmer was announced on Friday as the Premier League's latest Player of the Month. The 22-year-old produced an assist and five goals during September, including a stunning display in a 4-2 win against Brighton that saw him find the net four times.
Maresca is the first Chelsea boss to win the Premier League's Manager of the Month prize since Thomas Tuchel in October 2021.
Meanwhile, Palmer has now won two Player of the Month awards in 2024, having earlier been recognised for his standout performances in April.
Cole Palmer, who hit four goals in a 4-2 win over Brighton, won the Player of the Month prize
Maresca paid credit to his team of backroom staff after learning of his individual award.
'We had a very good month,' said the former Leicester boss.
'We all need people around us to make things better. I'm very grateful to have all of them.
'We are always looking at new things and how we can improve from different football and different countries.'
Palmer received his September Player of the Month while on international duty with England.
It was his second award of the week after he had earlier been confirmed as the England Men's Player of the Year.
But Palmer and his international team-mates had a night to forget on Thursday when they fell to a 2-1 defeat by Greece at Wembley in the UEFA Nations League.
Palmer played the full 90 minutes but was unable to inspire a positive result, despite having 88 touches - more than any other player apart from defender Levi Colwill.