AUDIO: We’re not going to give up - Chris McCann
But he insists the squad haven’t given up on a play-off place yet.
The gap to sixth place Cardiff is now nine points, with 11 games remaining - but next up on Sunday is a trip to the Welsh capital.
And McCann said: “We’re not going to give up, we’re never going to throw the towel in.
“There are still 11 games to go, and even though we need a lot of points to get into the top six, our aim is still to finish there.
“I don’t think you can let your season peter out, you’ve got to go for it, and hopefully we can get the right results.”
But he felt Burnley let Palace off the hook at the Turf, having taken an early lead through a Jay Rodriguez penalty, only for the Eagles to win a point with Darren Ambrose’s spot kick on the hour: “I think the way we played and the way we started the game, was good.
“Getting ourselves 1-0 up and dominating most of it - particularly in the first half, when I thought we controlled pretty much all the play.
“If they were going to get anything from us it would be through our own fault.
“They nicked a penalty, which I don’t think was a penalty looking back on it.
“He (Wilfried Zaha) did a couple of stepovers and I think he was on his way already, so the boys are feeling a little bit hard done by with the decision.
“But you can’t really look back on that. I think we had enough of the play to take more chances and do more damage to them and we didn’t do it.
“For all our dominance we didn’t capitalise enough on it and penetrate them enough.
“Danny Ings’ was I think the only chance we really had to make it 2-0 almost straight after the penalty, but the keeper made a great save.
“Apart from that we didn’t hurt them enough.”
McCann added: “I thought we did alright, and on a different day we could have taken all three points.
“But after the run we’ve been on, we’re going to take the point.
“After the last couple of defeats I think we’ve got to start somewhere.
“Three points would have been nice, especially for the day it had been.
“But we’ll take a point and move on.
“We look at the games coming up and hopefully we can carry that on in the next two games.”
McCann admitted it was a tough afternoon, after hearing the sad news about the death of Eddie Howe’s mother Annie.
Howe missed the game on compassionate leave, and McCann said: “It’s going to be tough with the gaffer not here and all our thoughts and well wishes are with him at this time.
“It must be a tough period to be going through.
“We only found out on the morning that she passed, so it was a massive blow to everybody.
“It’s a difficult period but we are fully supportive of him and we will be ready to take him back when he is ready to come back.
“We’ve got a job to do here and we just want to do him proud when he’s not here.”