The Clarets were looking for a fifth straight home win as they welcomed Bournemouth and their manager Eddie Howe, who left Burnley last November to return to the Cherries.
It looked like it would be the happiest of returns for Howe as Tokelo Rantie's superb 25-yard strike five minutes after half-time appeared to be handing Bournemouth a first-ever win at Turf Moor.
But the in-form Danny Ings rescued Burnley with an 84th-minute equaliser, stretching his side's unbeaten run in the league to 12 games.
Dyche admitted there was a little regret at his side's failure to again take all three points but that was eclipsed by his pride.
"I was really happy with the way we kept going to force a point," Dyche said.
"Tom [Heaton] has hardly had a save to make. He had one in the first half which was for the cameras and a good take from one slung in from 35 yards so there were good signs.
"It's hard because teams come here and they want to do well. There is a mild tinge of disappointment but I've told them that they're top of the league, they've taken 26 points out of 30 so I said I wouldn't be too disappointed.
"It's hard to win football matches all the time but we've shown great quality again.
"We're plus-17 goals so we can't be too hard on the players just because there was a couple which didn't go our way."
After a goalless first-half Rantie lit the game up as he turned his man 25 yards from goal before unleashing a drive that cannoned in off the bar.
But it was not enough for the win as with six minutes left substitute Junior Stanislas lofted in a measured ball which Sam Vokes flicked on for his strike partner Ings to nod home.
Bournemouth manager Howe said: "I think when you're 1-0 like we were with the time left in the game you're disappointed not to win but I thought it was a really honest game between two really honest teams.
"Burnley play very aggressively on the front foot and put a lot of long balls into your box and you have to defend them and I think if there has been a criticism of us this season it has been defensively in the area but I thought we responded very well here.
"We scored a terrific goal and with the time left we were hoping we could win it.
"I think we do have goals in us going forward but improving the defensive record is the priority.
"We adjusted our style of play today and I think we had to because if we had our usual free-flowing football it would have been a difficult game for us.
"Burnley press the life out of teams and we didn't want to walk into that.
"It was an emotional day. It meant a lot to me to try and get a display. I was really pleased with the reception we got from Burnley supporters."