The quartet issued a statement via the Baggies' official website:
"We would like to take this opportunity to apologise to our team-mates, the Head Coach, the Club and especially the supporters for the events which have been the subject of widespread and negative publicity.
"We felt it important we identify ourselves as the players involved in an incident which occurred during the training camp in Spain this week out of respect for team-mates who otherwise could be implicated by association.
"We freely acknowledge and apologise for the break of curfew which we accept represented a breach of the standards of professionalism required of us as representatives of West Bromwich Albion FC.
"The Club has informed us that it will now conduct its own inquiry into the incident and we will co-operate fully.
"In the meantime, we would like to assure our supporters that this incident does not reflect the determination and resolve we possess to do all we can to recover a difficult season."
The infractions occurred while West Brom took a trip to Spain.
BBC Sport's Matt Davis detailed the issues. Davis noted how four of the Baggies' senior stars were interviewed by Catalan regional police after taking a taxi without permission to return to the team hotel after finishing at a restaurant at around 5:30 a.m.
The incident does not reflect well on a squad rooted to the bottom of the Premier League. West Brom are seven points adrift of safety, a position making manager Alan Pardew more reliant on his squad's most experienced players.
It's what is likely to disappoint Pardew and owner Guochuan Lai the most that senior players such as Evans and Barry were involved.
Evans, 30, is the best defender at Pardew's disposal, while 36-year-old holding midfielder Barry would be expected to act as a leader for a struggling group.
As BBC Sport's Simon Stone pointed out, the gesture of an apology can't mask the underlying concern about the attitude and application of West Brom's top players:
Lai recently sacked chairman John Williams and chief executive Martin Goodman, putting the pressure firmly on Pardew. The manager has revealed he feels "let down" by the players' dubious actions, per Goal's Dom Farrell.
The fact this incident occurred less than two days before the Baggies take on Southampton in the fifth round of the 2018 FA Cup only emphasises the challenge facing Pardew to motivate a distracted squad.