The 36-year-old was joined on the scoresheet by Loum Tchaouna, Jaidon Anthony and Jaydon Banel before the Lions grabbed a consolation goal deep into added time through substitute Josh Coburn.

Parker praised Barnes not only for his performance but his tireless work behind the scenes and hopes he will be a catalyst in his side elbowing towards Premier League safety in the months to come.

“He sets an incredible example,” said Parker.

“I’m so pleased for Ash because he’s an experienced guy and at this present moment, when we’re having a bit of a tough time, the help he gives me and the coaches and this young squad, he’s a really positive guy.”

Despite making eight changes to the side that started in Wednesday’s 2-2 draw against Manchester United, Parker was rewarded with a thoroughly dominant display that he hopes will help point the way upwards.

He added: “We’re in the Premier League where it’s a different level, but in saying that this is tough opposition we played, a team who have got some really good results in the Championship and are fighting for the play-offs.

“So I’m pleased with the changes we made, we still looked strong and I’m hoping that after two good results, at Man United and a positive and dominant performance today, that can breathe some confidence into the team.”

Millwall boss Alex Neil admitted his side deserved nothing from the game and intends to quickly re-focus on their push to establish themselves in the Championship play-off zone.

Neil made seven changes to the starting line-up from last week’s win over Swansea, but after a relatively stable first half-hour they were ultimately undone by a series of defensive blunders as they fell to their heaviest defeat of the season.

He said: “It’s always disappointing to lose a game in that manner. I think the first half was frustrating because there were bits when we had some good play and some good territory.

“The biggest difference was how clinical Burnley are in the final third, versus how clinical we were, certainly in the first half.”

Neil insisted he had no regrets about ringing the changes, with the likes of Femi Azeez and Mihailo Ivanovic left out of his travelling squad.

“We’ve left five or six first-team players back down the road and the reason we’ve done it is we’ve suffered from injuries all season and we’ve still managed to mount a challenge,” Neil added.

“Our priority is obviously going to be the league. We’ve had a great season and from this point we’ve got an opportunity to go and try to finish the season well.

“I think with the injury list we’ve had this season, to list some of the first team lads I didn’t list today would have been negligent from me.”