Sunderland could have climbed out of the bottom three with a win and did enjoy the better of the chances at the Stadium of Light on Saturday, but ultimately the hosts had to settle for a point.
With games in hand over all of their fellow relegation battlers, Sunderland can still claim to have their fate in their own hands.
And Poyet was happy with the performance against Palace.
"I am very calm," he said. "We tried everything today, that's what type of team we are and that's the team that we have. If we play like that only the future will tell if we are good enough to stay in the Barclays Premier League or not.
"Today was the right way to perform, we take risks to try and win games. We take control and try to make crosses, with free-kick, shots, playing in behind and one-twos.
"We tried everything but we didn't score that's the most difficult part of the game. We couldn't score but I will go home very calm today.
"I am calm because I know the players gave everything for this football club and for the fans, so we will now see next week."
Sunderland, who have won just one of their last eight home matches, face a trip to Norwich City next and Poyet is hopeful their fortunes will change.
"The problem at the moment is that that inch is just not going our way, if we score early in a game then it is completely different," he added.
"So we need to be smart but we know what it takes, it's not going to be easy but if we try like we did today and play like we did today then we have a great chance that's for sure."
