Ashley Barnes' scrappy 62nd minute goal cancelled out Badou Ndiaye's first half strike as the Clarets strengthened their grip on 7th spot in the Premier League.
"It was a hard-earned point," Dyche said, quoted by Burnley's official website. "As people would have expected, they are fighting for their lives here and working hard as a team.
“In the first half they were the better side; not by a long way but definitely the better side, but in the second half we changed it around."
Burnley could have gone in 2-0 down if Mame Biram Diouf had converted a gilt-edged chance on the stroke of half time, but they responded well after the interval and would have won had it not been for a man of the match display from Stoke keeper Jack Butland.
“We told the lads we had a good number of points on the board and to go out and play with that freedom and use it wisely," said Dyche.
6 - Ashley Barnes has scored six goals in his last eight Premier League games, as many as his previous 44 combined. Bounce.— OptaJoe (@OptaJoe) April 22, 2018
“We got on the front foot and ended the game really strongly. In a way they were throwing bodies forward and trying to nick it and that did leave them open in transition and we work very well in transition."
Burnley's best result of the day came not at the Bet365 Stadium, but at Wembley, where Chelsea's win over Southampton in their FA Cup semi final means that the team finishing 7th in the Premier League will qualify for next season's Europa League.
One more win for Dyche's men from their remaining three games will guarantee Burnley's first European campaign since competing in the 1966-67 Inter-Cities Fairs Cup.
Burnley can seal the deal when they host Brighton next Saturday.