The La Liga champions had recorded a 3-0 win in the first leg semi-final tie at Camp Nou, before going down to the Premier League side in the reverse fixture.
Messi, who bagged a brace in the first leg, said the biggest mistake was failing to compete during the 4-0 defeat which sent them crashing out of the competition.
“It was as painful as losing the 2014 World Cup final with Argentina,” the Argentina international said during his first media appearance since the loss.
“The first half wasn’t all that bad, but in the second (half) we didn’t even compete.
“There was only one team on the pitch and that was the biggest mistake we could have made,” Messi said ahead of Saturday’s Copa del Rey final against Valencia.
“The worst thing we could do, and what we cannot forgive ourselves for, is the fact that we did not compete. We let them walk all over us.”