The pair, who paid £628 for flights from Luton to Sicily, claim they were told by staff after boarding the plane they would have to leave because it was overstaffed.
Staff allegedly did not tell them of their right to a replacement flight that day or compensation and said there would not be another flight for four days.
Easyjet has apologised and blamed the incident on an error, saying they should not have issued boarding passes to the couple.
Viddha, 35, and Manoj, 38, and told the Independent they had planned a six-day break, booking £1,270 of non-refundable accommodation and transfers in Sicily. In the end, they had to cancel the trip.
Manoj told the paper: “This was an incredibly humiliating situation.
“The airline had overbooked and we were involuntarily off-boarded from the aircraft by two airport staff in front of a packed plane.
"The only difference between us and the chap involved with United Airlines is that we weren't physically dragged off.”
A spokesman for Easyjet said: “The circumstances were very unusual and resulted from a manual error at the gate.
“We have listened to our call recordings and at no point did we refuse alternative travel or EU261.
“We want to reassure our customers that we will be providing additional training to our contact centre agents to make sure that future customers are not put through a similar experience.
“This should also have been handled better at the airport on the day so this has been picked up with the individuals concerned. We are genuinely sorry for what has happened.”
The incident occurred last Monday, just a day after shocking footage showed Dr Dao being dragged screaming from an overbooked United Airlines plane.
Dr Dao, 69, is taking legal action over the incident, which saw him lose two teeth and break his nose.