Zian Flemming's header in the third minute of second half stoppage-time earned the draw, after Joao Pedro had earlier handed Chelsea - who were reduced to ten men when Wesley Fofana was dismissed 18 minutes from time - a fourth minute lead.
Parker said afterwards: “It was a really resilient, battling performance. This team never gives up. We showed that today and we showed that at Palace ten days ago.
“The noise has been really intense over recent weeks - but the togetherness, spirit, mentality and resilience of this side shone through again today.
“When they went down to ten, we managed the game really well. Our application and execution during that final 20 minutes really impressed me.
“We showed incredible desire to keep going and we were rewarded with a deserved point at the end.
“Of course we’re pleased with a point – but we’re probably a little bit regretful that we didn’t nick it late on.”
Flemming goal
Parker was eager to highlight James Ward-Prowse's free-kick ability for Flemming's goal.
He also said, “It was a fantastic goal.
“Prowsey’s delivery was on the money and Zian headed it home in some style. It’s an incredible set piece goal – straight off the training ground. A first class set play.
“It was worthy of the point we gained – and was thoroughly deserved."