Lionel Messi hit his 100th Champions League goal to consign Chelsea to a 3-0 defeat at the Nou Camp
Chelsea manager Antonio Conte felt the 3-0 defeat in Barcelona which ended his side's involvement in the Champions League was "unfair".
Two goals from Lionel Messi plus one from Ousmane Dembele - his first in a Barca shirt - helped the Spanish giants to a 4-1 aggregate victory.
Defeat damages Chelsea's chances of Champions League football next season, with Conte's side now needing a top-four finish in the Premier League.
"We have no regrets," he said.
"If you watch the game, you can see the final result is unfair."
Conte acknowledged Messi - who also scored in the first leg - had been "the difference" between the sides.
The Argentina striker's second goal in the Nou Camp took him to 100 in the Champions League.
While Real Madrid's Cristiano Ronaldo holds the record with 117, Messi reached three figures in 14 games fewer.
"We are talking about the best player in the world," said Conte.
"He scores 60 goals every season - he is a super top player. Barcelona were very clinical."
'Extraordinary and joyous' - Messi joins the Champions League 100 club
Football Daily: 'Chelsea handed it to Barcelona on a plate'
Relive Wednesday's match at the Nou Camp
Sixteen become eight...
This season's Champions League quarter-finalists are: Barcelona, Bayern Munich, Juventus, Liverpool, Manchester City, Real Madrid, Roma and Sevilla.
The draw will take place in Nyon, Switzerland at 11:00 GMT on Friday - and you can follow it live on the BBC Sport website and app.
Chelsea led for 13 minutes of the first leg and hit the woodwork four times over the two matches.
N'Golo Kante and Marcos Alonso both went close in the Nou Camp, before Antonio Rudiger headed against the bar in the closing moments.
The Blues also had appeals for a penalty waved away when Alonso went down inside the area under a challenge from Gerard Pique.
"We didn't deserve to lose 3-0," said Conte. "We were a bit unlucky.
"I think we created many chances but we didn't take them.
"I must be very proud about my players - they gave everything and we have to continue in this way, with this will to fight and desire to fight together."
Dejected Chelsea players walk off the pitch after defeat in the Nou Camp
'I don't think we deserve to be out'
Chelsea goalkeeper Thibaut Courtois told BT Sport: "I don't think we deserve to be out, but individual mistakes cost us in both legs.
"The first goal... I didn't expect Lionel Messi to shoot from that angle and I was too late in closing my legs. It was a mistake on my part.
"The weakest point is between the legs of a goalkeeper. It is annoying. I cannot hide inside, I have to be a man and come out."
Chelsea wing-back Marcos Alonso told BT Sport: "We knew they have top players and we cannot give them one metre because they can create and score.
"We have to improve and when you lose, you have to train and get better."
'You can't make mistakes like that against Bury, never mind Barcelona'
Former Chelsea striker Chris Sutton told BBC Radio 5 live that Conte's main irritation would be the manner of the first Barcelona goal.
"The frustration will be that there was all the talk was of this perfect performance [that was needed] and it unravelled so quickly with such a poor first goal with the error that Thibaut Courtois made," he said.
"You can't make mistakes like that against Bury, never mind Barcelona.
"You get brutally exposed at this level by the top sides."
Sutton added Conte "did not lose his players" but the Italian's position looks increasingly perilous.
The Blues are fifth in the Premier League, with games against top-four rivals Tottenham and Liverpool to come before the end of the season.
"The biggest problem you have at Chelsea is who is signing the players? There was Michael Emenalo who went to Monaco and that is probably Antonio Conte's biggest argument," Stoke City midfielder Charlie Adam said on BBC Radio 5 live.
"Whoever comes in will want full control [of recruitment]. If they bring in Luis Enrique, will he be happy to just coach the team?"
What next for Chelsea?
Antonio Conte takes his side to Leicester on Sunday, with a place in the FA Cup semi-finals is at stake
Sutton, who played for the Blues in the 1999-2000 season, said: "I just wonder where Chelsea and Antonio Conte go from here?
"It was only two years ago they were 10th in the Premier League and Conte transformed the team and they won the Premier League, so things can change.
"Will the owner accept fifth place under Conte with all the other issues? The chances are he won't be there at the end of the season."
Former Blues winger Pat Nevin said: "They played OK tonight but they were beaten by the best player that's ever played.
"Lionel Messi was astonishing over the tie - he had a hand in all of the Barcelona goals, either scoring or making them.
"The right team went through because they have special players and a special player."
'No shame' - your reaction
Bayo Omisore: No tears. No shame. It's Barcelona after all.
Jamie: Never seen Antonio Conte smile after losing a game, but even he had to ruefully smile when shaking Leo Messi's hand at the end.
Philipp: Much rather lose at the Camp Nou by three, than at Old Trafford against Sevilla. Best I've seen the Blues play in a long time. Can't excuse defensive errors, but should give confidence in the league.