Paul Clement’s side secured a 0-0 draw with the Cherries at the Liberty Stadium to end a four-game run of losses.
The South Wales outfit failed to find the back of the net in their third consecutive top-flight tie, an unimpressive feat that could have been avoided had referee Stuart Attwell not ruled out Wilfried Bony’s goal in the 44th minute after Ayew’s pull on Nathan Ake.
But the Ghana attacker is confident the result would set the standard for the lowly-placed team.
"We feel we should have three points, but at least we have one and we didn't lose the game," Ayew told club website.
"We tried our best to win but when things are not going your way, it sometimes doesn't happen.
"I think it was our best performance of the season - the gaffer said that. It's something to build on and hopefully, we can take into in the next games. We have set the standard now."
Ayew has featured in all of Swansea’s 13 top-flight games and has a goal to his credit.
In their next English Premier League encounter, the 19th-placed side will take on Chelsea at the Stamford Bridge on Wednesday as they look to build on the momentum gathered over the weekend.
