Jonny Evans, Gareth Barry, Jake Livermore and Boaz Myhill have come forward as the four West Brom players involved in a "curfew breach" during a warm-weather training camp.
West Brom are bottom of the Premier League, seven points adrift of safety, but were taken to Spain this week by head coach Alan Pardew in a bid to revive the club's flagging fortunes.
According to a report in The Sun newspaper, a group of West Brom players allegedly drove off in a taxi from a McDonald's drive-through without the driver and abandoned the car outside their hotel.
Facing the media on Friday, Pardew confirmed West Brom would investigate the incident and said he felt let down by the players involved, although he did not name them.
But in a statement released by the club, captain Evans confirmed himself as among the foursome, although no details of the incident were provided.
"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," Evans, Barry, Livermore and Myhill jointly said.
"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 Brom.
"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."
Northern Ireland international Evans was linked with a January move to Manchester City and Barry and Livermore are both England internationals, the latter midfielder having been capped by his country as recently as 2017, while goalkeeper Myhill is a former Wales international.
West Brom chairman John Williams and chief executive Martin Goodman were sacked by owner Guochuan Lai earlier this week, while forward Jay Rodriguez is fighting a Football Association charge over an incident with Brighton and Hove Albion defender Gaetan Bong in January.