Kieran Trippier says the Clarets were left to rue missed opportunities again after the 0-0 draw with Stoke City.
Stoke City and England U21 goalkeeper Jack Butland was called into action on several occasions in the first-half, first to stop Danny Ings after a mazy run and later denying David Jones from close range.
And despite being pleased with a successive defensive shutout, Trippier felt Burnley should have claimed all three points in the final home fixture of the season.
He said: “We defended well today and at times it’s been a touch frustrating this season when we’ve conceded from corners or sloppy goals.
“We had to be brave and we dealt with a different threat in Peter Crouch well when he came on so we’re happy with that as a defensive unit.
“If you look at the opportunities we’ve had in many of the games this season, we probably should have put them away but we didn’t and that’s cost us.
“Other teams take their chances and that’s why we’ve not got as many goals and as many points as we wanted this season.
“People will have seen how we played today and we pressed them well and we had a lot of opportunity to score but we’ll take the point and move on to Villa now.
Reflecting on the season as a whole before next week’s curtain call at Aston Villa, Trippier added:
“I think we’ve shown everyone what we’re about this season. We’ve been in every game, we work extremely hard and we go to win.
“We’re all disappointed to go down but hopefully we can bounce straight back next season.”