Coming off the back of three games unbeaten to start the season, the Eagles began the match brightly at Eppleton Colliery Welfare Ground, Elise Hughes heading in her sixth goal of the season with just eight minutes on the clock.
But with both teams spurning further opportunities across an absorbing 90 minutes, Palace found themselves pegged back in the final minute of regulation time, Brianna Westrup converting from a late free-kick for the Black Cats.
Everett told cpfc.co.uk: “It was a tough one to take, conceding late on, but at the start of the season we would’ve taken four games unbeaten, so it’s something to take confidence from and draw the positives from, rather than negatives.
“Today we didn’t play how we wanted to play, but we ground it out and got the point in the end, which is good.
“Going into the international break and leading up to Sheffield United [on Saturday 30th September], we’re just going to regroup, focus on this game and reflect on what we can fix for that one.”
Everett said of Hughes: “It helps the backline when you’ve got forwards who can finish like Elise and put the ball in the back of the net. It relieves pressure on us as a team.
“Looking at that game, we had chances, they had chances, and I think coming away from it, it was probably a fair result.”
Palace sit third in the Women’s Championship table after four games played, with the September international break now ahead of them.
Following the two-week pause, Palace return to action against Sheffield United Women in south London at the VBS Community Stadium on Saturday, 30th September (14:00 BST). Click here for more information.
Tickets are now also available for the clash against London City Lionesses on Sunday, 15th October (14:00 BST) and for the fixture against Lewes on Sunday, 12th November (14:00 GMT).