Nahki Wells was an unused substitute as Burnley are virtually assured of European football next season for the first time in over 50 years after picking up a point in a 0-0 draw with Brighton.
Everton's victory at Huddersfield means the Clarets are not mathematically assured of a top-seven finish, and a place in next season's Europa League, though they are six points clear of the Toffees with two games remaining, and have a far better goal difference.
Burnley, whose last European campaign was during the 1966-67 season, came closest to scoring at Turf Moor when Kevin Long hit a post in the first half, yet Brighton also picked up a valuable point in their battle to avoid the drop.
Reggie Lambe was not in the team as his Carlisle teammates came from behind to secure a 2-1 victory at Port Vale in Keith Curle's penultimate game as manager.
Curle, who is leaving the club at the end of the season, saw second-half strikes from Ashley Nadesan and Hallam Hope cancel out Dior Angus' opener.