The quartet were interviewed but not arrested by police after the incident, which happened in the early hours of the morning and is being investigated by the Premier League club.
“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.
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 “the events which have been the subject of widespread and negative publicity”.
Mossos d’Esquadra - the Catalan regional police force - had told BBC Sport the four players involved wanted to go out in Barcelona, but found everything closed so took a taxi to a fast-food restaurant.
When they left, at approximately 05:30, it is alleged they took the taxi and drove back to their hotel - without the driver.
Police were alerted by the hotel and taxi driver, who was reunited with his vehicle at about 08:00.
Baggies boss Alan Pardew said the players involved had broken a midnight curfew, adding it was “unacceptable” and he “felt a bit let down”.
“It wasn’t what we wanted,” he said. “We’ve gone there to try to get ourselves ready and up for the run-in and this is obviously not ideal.”
West Brom, who are bottom of the Premier League, have won just one of their past 25 league matches.
They host Southampton in the FA Cup at 15:00 GMT on Saturday