Gareth Barry, Jonny Evans, Jake Livermore and Boaz Myhill were questioned by police, but not arrested, after driving themselves back to their hotel in the taxi in the early hours of Thursday morning.
West Brom and Northern Ireland defender Evans 30, former England midfielder Barry 36, England international Livermore, 28, and reserve goalkeeper Myhill, 35, said they wanted to apologise for "breaking the curfew" and for "the events which have been the subject of widespread and negative publicity".
"We felt it important we identify ourselves out of respect for team-mates who otherwise could be implicated by association," they said in a statement.
The four had left their hotel at around 5.30 am in search of somewhere open for food. They hailed a taxi to McDonald's Drive-thru and then allegedly drove themselves back to the hotel.
Catalan police force, Mossos d'Esquadra, had tracked down the quartet back at the hotel and returned the taxi to the driver at about 8am.
West Brom, who are bottom of the Premier League, were in Barcelona for a training tour.
The players added: "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 club said it had "instigated its own investigation into the incident" and said the players "will be subject to the full rigours of our internal disciplinary procedures".