Palace remain bottom of the Premier League table but are level with Sunderland, who stay in 19th as they have scored more goals than the Eagles.
However, Bolasie reckons Palace had enough chances to overcome Roberto Martinez's side and was happy with the team's performance.
"Overall, we had the better chances. We were unfortunate today but hopefully our luck will turn next time," he said.
"It's very important (to keep a clean sheet), the lads have come in feeling good and that's the way we want to be feeling instead of losing every week."
Bolasie says that Palace showed their true team spirit which he hopes will impress any prospective manager.
He added: "The spirit was there as you could see, and the fans were helping us as well. They have been there whether it's been bad or good.
"I'm happy we got a point, even though I think we deserved to win it, but that's football.
"Any manager can work with our team, we've got a lot of talent and team spirit."