Neither side are yet to score or win in the league this campaign, but Swansea won their Carabao Cup match 4-1 on Tuesday and Ayew wants them to build on that ahead of their trip to Selhurst Park.
However, the last time Palace lost their first three opening games they ended up getting promoted under Ian Holloway, so a disastrous start may not be the end of the world for the Eagles.
Christian Benteke was isolated up front all afternoon although Palace improved after De Boer switched to a back four following Swansea's second goal. I cannot say we are in a very good situation right now.
Although Swansea also had not scored in the league prior to this victory, manager Paul Clement now believes his side can consider this a good start to the season.
"That is the Crystal Palace I want to see, we created chances then and Swansea did not".
The first chance of the game fell to Ayew, latching onto the end of Abraham's cross but his header flew just wide of the goal.
"We've had a hard start with two of our three Premier League games away from home and we were away to MK Dons in the cup".
Abraham sent the home crowd roaring as an attempt from the 38th minute after a mistake from Timothy Fosu-Mensah could've led to an away goal, but Wayne Hennessey saved the Eagles from the in-form Chelsea youngster.
Swansea took the lead through Abraham, who fought off Martin Kelly to score with the Welsh side's first shot on target of the season.
The 25-year-old has maintained his place in the side in the early stages of the season, with three starts in three games in all competitions, and has been one of the club's biggest attacking threats. "Especially in the first half, we didn't show any courage on the ball".
The half was meandering to a close when Swansea scored with the first on-target attempt of the game.
However, Swansea stuck again through Ayew after Kyle Naughton intercepted possession and set the striker through on goal for him to beat Hennessey.