United took the lead early on through Javier Hernandez, with initial play looking encouraging from their perspective, but an Aras Ozbiliz equaliser, followed by Toby Alderweireld’s late winner, turned the match on its head.
Sir Alex Ferguson’s men still managed to progress to the last-16 of the competition, holding on to an aggregate scoreline of 3-2, but Jones was extremely disappointed with the performance and result after the match.
Speaking to Channel Five, Jones said: “I don’t think we were at our best tonight, everyone can see that. We got off to a great start, Chicha’s [Hernandez] scored a great finish and we were in control of the game.
“A little bit of complacency crept in and it has cost us. We should have won the game.
“We’ll probably review our performances tomorrow, then take it from there.
“It wasn’t good enough in the second-half, nowhere near.”
In the build-up to the clash, United boss Ferguson had demanded that his players remained focussed for the match despite the 2-0 lead from the first-leg, but Jones has admitted the Red Devils failed to follow the 70-year-old's instructions after half-time.
He continued: “He just said we’ve got to move the ball quicker and up the tempo. We didn’t do that, for whatever reason, we’ll review that tomorrow."
Thursday also saw Jones called up for England’s friendly with Netherlands, while he was quick to praise team-mate Tom Cleverley, who looks set to win his first cap for the national team after also being included in the squad.
“Regarding that [another England call up], I’m delighted to represent my country,” he said.
“It’s an honour. And a place for Tom Cleverley too who has been out for some time and he is a great little player.”
Before the match, there was confusion in the United ranks over who would be leading the team out as captain with Nemanja Vidic, Rio Ferdinand, Patrice Evra and Ryan Giggs all missing from the line-up.
Initially it seemed Jones would be given the armband, but it wasn’t to be in the end as Ji-Sung Park stepped up to the mantle.
He went on: “Mick [Phelan] came to me before the game and said I was captain, but I think the gaffer meant Ji [Ji-Sung Park].
“I don’t really think it matters who is captain to be honest. We’ve lost the game tonight and we are bitterly disappointed.”
After progressing, United will face Spanish side Athletic Bilbao in the next round of the Europa League, with the Basques visiting Old Trafford on March 8 for the first-leg.