West Ham fell behind in the 42nd minute at Selhurst Park through Marouane Chamakh's header and they offered little after the break apart from a disallowed goal from Stewart Downing.
Jaaskelainen was disappointed with side's failure to mount a fightback and has called on the Hammers to raise their standards in time for Saturday's Premier League trip to Liverpool.
He told the club's official website: "We put in a great performance on Saturday and obviously we wanted to build on that and carry on, but it was frustrating on Tuesday because when you go 1-0 down you want to have a good response.
"You can't go 1-0 up in every game so the response is important - we still had 50 minutes to get a goal and then go on to try and win the game but it didn't happen.
"They hadn't really created any chances up until then, and they've got a new manager who everybody knows is very keen on set plays. It was always going to be key for us to be good on the set plays, but we've conceded from one.
"We have to make sure that we have a good game and a good response at Liverpool now."
West Ham's lack of attacking bite was surprising after the 3-0 win over Fulham at the weekend and Jaaskelainen insists his side must be more ruthless at Anfield.
"You know that you have to be ready for the situation [of coming from behind], so hopefully we can learn from what happened at Crystal Palace," he said.
"It has not been an ideal start but we have a chance to get back to a good performance on Saturday.
"We took our chances on Saturday and we need to do that consistently, hitting the target and making the goalkeeper make saves.
"We've defended the corners and wide free kicks very well throughout the season, so we need to put Crystal Palace behind us, and build on what we achieved against Fulham."