Ben Mee admitted a sluggish start had cost the Clarets as Everton completed the double over Sean Dyche’s men.
Two goals in the opening 20 minutes proved too great an obstacle to overcome as Burnley lost their last away game of the season 2-0 at Goodison Park.
But with Premier League safety already assured, Mee hailed the collective effort the Clarets have shown since a 5-1 home defeat to the Toffees on Boxing Day had left them deep in relegation trouble.
“The lads have been fantastic overall,” said the defender, who is now just one game away from completing an ever-present record.
“We always do things right and we want to do that all the way to the end of the season.
“It’s been a big effort; a massive effort from everyone at the club, from the position we found ourselves in, and it’s up to us now to see out the season strong.”
The Clarets finish their campaign at home to Arsenal on Sunday week when they will be looking to avoid a hat-trick of defeats since guaranteeing their top-flight status.
After pushing title favourites Manchester City all the way before losing 1-0 last weekend, Burnley were too slow out of the blocks against an Everton side still hoping to secure European football by finishing seventh in the table.
The Toffees set up a fourth successive home win thanks to a deflected goal off Mee before Seamus Coleman nodded in the second.
And despite fighting back after the break, Dyche’s side couldn’t find a goal to unsettle the Merseysiders as substitute Matej Vydra was denied a clear looking penalty following a shove from ex-Claret Michael Keane.
“The first 20 minutes cost us. We didn’t get going at all and they started strong with the crowd behind them,” added Mee.
“We couldn’t get out of our half for 20 minutes and they scored two poor goals from our point of view.
“It’s a tough place to come and, being their last home game, the crowd were up for it, so we found it difficult.
“We always do things right as a team and as a club and we were just a bit off it early in the game.”
The Clarets were also out of luck with Mee diverting a Richarlison shot past Tom Heaton for the opening goal – the only false step from the defender who continued his outstanding run of form with another top-class showing.
“It was disappointing, but you have to try and get in the way of shots,” he said.
“Maybe it was a bit of a leg dangled, but you have to try and get in the way. I try and get in the way of everything I can and unfortunately it took it back into the goal.”