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.'