The Clarets fought back from 2-0 down inside 33 minutes to lead 3-2 at halftime and held on throughout the second-half.
“It’s a fantastic feeling. I’m so happy for this group," Parker remarked afterwards. “We’ve all been hurting. We’ve been on a tough run.
“But that performance showed what I’ve said about this group. There was fight, spirit, commitment and resilience in abundance to come back from 2-0 down. Not many teams would be able to do that given the run we’ve been on.
“You don’t get that result tonight without a proper resilience - and the ability to stand up and fight. We’ve pulled off a brilliant result - everyone deserves huge credit.”
On defending their lead, Parker also said: “We had to survive a bit in the second half. We dug deep. We had to hold on at times but I thought we defended rock solid in the second half.
“Martin (Dubravka) came up with a huge save late on, that was key for us, and saw us over the line.”
Parker also said: “We’ll keep fighting. We’ll keep believing.
“We won’t dwell on the past. What’s happened has happened. We’ll focus on the present and what’s to come.
“I’m delighted for our fans tonight. On a wet and cold and miserable night, we’ve given them something to head home happy about.”