Armando Broja struck a first goal for Burnley on 90 minutes to cancel out Antoine Semenyo's strike midway through the second-half.
Parker remarked afterwards: "It’s a brilliant point for us. We needed to end the run we were on. The players were worthy of their point.
"We were really competitive and gave ourselves a fighting chance, and we were well worthy of the result in the end.
"I’m delighted for the subs who came on. It was a great cross from Marcus (Edwards) and a brilliant finish from Armando.
"They both made a massive contribution and I’m delighted for both of the lads, but overall I’m delighted for the group.
"Their goal came out of nothing. We’d really restricted them until that point.
"It was a slip - and then an incredible finish, which Semenyo is obviously well capable of. I didn’t feel we deserved that at the time but we stuck to the plan, took it on the chin and kept going.
"Our reaction to going a goal behind was incredible. That spirit is never in doubt with this group."