The Blues are on a terrific run of wins in the Premier League, pushing them up to sixth place.
With an outside chance of fifth still on the cards on the final day of the season, Palmer praised his teammates and manager Mauricio Pochettino after a win over Brighton.
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He stated: "We needed three points and it was hard towards the end but for it to be in our hands to get sixth place is a big thing for us.
"Marc (Cucurella) knows where I'm going to be and I lifted it (the header) over the goalkeeper.
"Chelsea is a big club and everyone wants to finish higher than sixth but you have to look at where we were at the start of the season so to get back into Europe would be a step in the right direction.
"All credit to the manager. All the players love the manager and want to fight for him."