Sean Dyche felt his side fell on the wrong side of Lady Luck as Everton consigned them to another away defeat.
The Clarets had the better of the first half as they sought success on the road against a Blues side that had won their last seven home league games.
They were on level terms early in the second half too after Sam Vokes’ penalty immediately cancelled out Phil Jagielka’s scruffy opener.
However, a deflected shot from Ross Barkley, that hit Michael Keane and Ben Mee and went in off the post, put the Merseysiders back in front, before Romelu Lukaku scored at Goodison Park for the ninth successive game to settle the outcome.
Clarets boss Dyche said: “You don’t want to cry it in about luck and they are a fine side who are going well at home, but when you see a semi-bobbly first goal and then what happened with the second, you come away frustrated.
“The second goal is so important and it hits two of our players and goes in, which is so unfortunate you can’t believe it.
“Before that we’ve had two cleared off the line and two one-v-ones and numerous other chances when we could have scored, so I am frustrated, but not with the performance because I thought that was decent.
“To come here against a side so in-form and edge the first half was really pleasing because they are a fine side.
“I still felt we were going well in the second half but we just lost our focus for two or three minutes and after that second goal we saw a striker in top form who finished it well.
“I thought we were in the game throughout, other than that two or three minutes, but that’s the Premier League and that can change a game, as it did today.”
Michael Keane had a first half header cleared off the line by the omnipresent Barkley, before Vokes was denied by Joel Robles.
And despite a 13th away defeat of the season, results elsewhere left the Clarets still eight points clear of the drop zone with just five games remaining.
Dyche, who was without Scott Arfield (knee), added: “As I said, I don’t want to cry it in because they are such a good side and in fine from, but it was a pleasing performance today.
“You have to have performances that mean something and we did that today, although it didn’t get us any reward.
“Our mentality stays strong though and the physicality and belief is very strong, so we just keep on taking the challenges in front of us because five points out of five games, after a tricky run, is a good return.
“We’ve had three clean sheets within that and a big win against Stoke, so this was always going to be a hard game.
“You can’t just change the rule book half way through the season, and performing like that will get us what we all want.”