And Palmer, who is part of the coaching team overseeing the final two games of the season, admitted he couldn't have asked for any more from the home players.
He said: "We asked for passion today and we asked for a performance. And we got both. Are we disappointed we lost? Of course we are. But the boys put on a good show today.
"We had the Aviva Premiership champions in town and there was so much resolve to try and get a result.
Palmer was also quick to pay tribute to the attitude of the players after the departure of Richard Hill earlier this week.
He continued: "Nigel and the coaches have been unbelievable in terms of refocusing the players on the rugby after a difficult week and you saw that from the reaction and performance.
"We really wanted to go out and win. The guys are professional and they've been nothing but professional all week. And the staff have been magnificent as well."
Warriors have a break next weekend before concluding their season at already relegated London Welsh.
And Palmer believes Worcester can finally get their first away win of the campaign.
He added: "There will be no trouble in picking people up. There's just a sense of frustration but the boys will regroup and then look towards Welsh.
"We want to get that monkey off our back in terms of our away record and finish with a bang."