Dyche pleased with performance in defeat at Everton
Burnley gave as good as they got at Goodison Park until 20 minutes from time when Ross Barkley's shot took two deflections off Michael Keane and then Ben Mee to drop inside the far post.
The Premier League's top scorer Romelu Lukaku put the result behind doubt moments later.
The Clarets had edged the first half before falling behind just after the break to a Phil Jagielka goal, before Sam Vokes deservedly levelled from the spot.
Dyche said: "It's a tough one to call about being hard done by, you don't want to cry it in, but I thought the performance was good.
"It was very good first half, these are a team on a real hot run at home, and not just edging games, they've been winning games outright.
"First half I thought we were excellent, to think we had one cleared off the line, two one on ones, their keeper made a good save, and they've not had much.
"Second half I didn't think there was that much in the game, which is pleasing in the overall picture, it's the details yet again, and that's the frustrating thing.
"That's what the Premier League is like, the details are so, so important, and a bit of the rub of the green, but they're a good side."
Barkley had the luck with his key goal, and Dyche admitted: "That was a real blow, there's not a lot in the game, they've scored one which gets a deflection off the centre half and goes to the back stick, and Tom is ever so unlucky not to keep it out, and we reacted very well.
"We got right back on the front foot as we had done all day, and the second one is really frustrating.
"We give the ball away far too cheaply, but even then, to get a shot that hits your centre half, it's going wide, then hits another centre half and goes in.
"That's got to be bad luck.
"They then have three minutes where they turn up the heat and one of the top strikers in the game scores a great goal, and that's the Premier League, that's how harsh it can be.
"We still responded, had another one cleared off the line, and attempted to get back in it, but it's difficult away from home at clubs like this."
The first half in particular was arguably as good as Burnley have performed away from home, as their search for a win on the road continues: "Well yeah, it's one of those strange things, and it's frustrating in that respect, if you're a neutral and didn't know we hadn't won away and saw that game, you wouldn't believe it I don't think.
"I was really pleased with the performance, not the result. To come to a place like this is difficult, so overall I was really pleased."
Dyche left top scorer Andre Gray on the bench to pair Ashley Barnes with Sam Vokes, and he explained: "I just thought we needed a bit more physicality up there, and I thought it showed, I thought the front two were good.
"I was pleased with that.
"I was pleased with the shape of the team, I was pleased with a lot of it, the basics were good, the shape, we've affected the game, played when we could, got it forward and made it uncomfortable for them when we could, and for big patches of the game knocked them out of their stride.
"So disappointed with the outcome, but not the performance."
Burnley remain eight points clear of danger with five games to play, and two trips away to break their duck: "It's a head-scratcher still, when you think of the times we've had away from home particularly, to put one to bed.
"Close today, but the league table doesn't change much.
"With that kind of performance, I think that's got to win you a game away from home at some point.
"One day, all the deflections and the rest of it have to happen for you.
"But you want to work for your luck, you don't want to rely on it, and we certainly don't."
Scott Arfield wasn't in the 18 after picking up an injury in training: "Scotty had a knock, right at the end of last week, a small problem with his knee.
"We think it will settle down and he'll be ok.
"Vokesy came off with a tight hamstring, so we'll see where that's at, but we have an extra day."
Dan Agyei came on for his second taste of Premier League football, has a late substitute, having made his debut across Stanley Park at Anfield: "We thought at that stage, try and introduce Dan, we want him to get a feel of what it is. He's earned the right, to be fair."