Barnsley came to Burnley having won at Brighton in midweek but a Michael Kightly goal twenty minutes into the second half settled this one.
"Obviously I'm disappointed," Mellon said. "We missed that clinical finish that's needed to get that first goal but I couldn't fault their effort, they gave me everything they have.
"We got an awful lot right in the first half, but I think from the 55th minute to the 65th minute we didn't win those second balls. I don't think in that ten minutes, we didn't role our sleeves up and weren't ready for the battle. In that ten minute spell we lost the game."
Having seen his side play well in the first half, he added: "If anyone came here today, they wouldn't have said there was anything between the two sides. If anything maybe we had the better footballers.
"We have to be more clinical and more aggressive in that final third. There's an awful lot to be pleased about and we'll get better.
"In this situation we're in, some might say we'd have to battle our way out of it. I think we can give our players responsibility and play, but we must need to take our chances. We never took them today, hence the result."
A first win in six league games for the Clarets and a place back at the top of the league. "In the end it's a well earned victory and it's brilliant for everyone, especially the community of Burnley," Dyche said after the game.
"It's very difficult to win as many games as we have, especially at home where we have been consistent since last March. That is outstanding and it's interesting because there was still a bit of impatience today from the crowd.
"I am getting to learn about our crowd. They have seen some brilliant things here this season, so it's important they allow the players that freedom to play. It's a shifting tide, a shift in mentality and a shift in expectation.
"I must make it clear, the fans are good in general. Today there was just that little impatience when we had a group out there working very hard.
"It's not easy to beat teams at this level, especially teams like Barnsley today. I said to the players afterwards that the toughest fight you will ever have is one against someone with nothing to lose. That was the case today. Barnsley came here and played with nothing to lose and everything to gain and we had to deal with a first half in which they played well.
"We were slightly below the levels we've set, but as every our framework got us a clean sheet. Tom had one big save in the first half when he was called upon, which has a habit of doing.
"I gave them a bit of a war cry if I am honest and that's unusual for me. It was just to jolt them and remind them how good they are and what we are trying to build here. There is a fantastic group in there with an honest endeavour and it was just taking the shackles off.
"In the second half we turned up the gas, got better and better and stronger and ran over them at times and it was a moment of real quality that won it from Michael. We know he has that quality and he has delivered it today to earn us the win."
Delighted with that return to the summit, he added: "We know what we are achieving here and I know how we are achieving it. There’s still more to come and I thought we showed great signs of that again today in the second half.
“It’s a tough ask in any game and it’s an interesting one today again people have been saying we were on a mini-slump. Going from first to third and back to first is a pretty impressive mini-slump and certainly the best I’ve been on.
“You don’t get everything your own way in this league, but in most of the games we’ve drawn we’ve been pretty dominant. We just had that one blip at Huddersfield, when we didn’t play well, but we know when we are playing well we can beat teams.
"It’s the results in games when you are not at your best that are the ones that are important over a Championship season . Today we found a way to win and that’s an important attribute to have.”