The passengers on Easyjet flight EZY6056 from Malaga to Bristol in the UK were still waiting to board when their flight took off.
They were just "metres away" from the plane, and their luggage was already in the hold when the plane departed, Spain's 20 minutos newspaper reported.
One of the 'forgotten' passengers, 58-year-old Iain Locke from Somerset told UK daily the Bristol Post that the group had been "trapped" in the corridor at the boarding gate.
"The stairwell was full, and people were getting on the plane, but then boarding seemed to stop," the passenger said.
"After wondering what was going on, I looked through the doors onto the airport apron and the plane had gone.
"I turned round to the guy beside me and said 'I don't want to alarm you, but the plane has gone."
"I just couldn't believe it," Locke told the Bristol Post.
"We were banging on the doors for about ten minutes trying to raise the alarm. It was a bit freaky being locked in there — especially for the people with young children."
Easyjet later blamed the incident on an "issue at the boarding gate".
The affected passengers had been contacted and apologies issued, an airline spokesperson said.
An investigation had also been launched and the passengers involved were given flight vouchers and a refund, the spokesperson added.
The carrier said 19 of the affected passengers took up the airline's offer of a later flight to London's Gatwick Airport.
Ten others stayed in Spain and flew on to Bristol on Sunday.