After taking the lead through Lautaro Martinez in the second minute, two second-half strikes from Luis Suarez would see the Catalans claim a narrow victory but Conte is adamant his side were hard done by.
Conte, who was warned by the referees about his conduct, particularly felt Inter should have been awarded a penalty for a foul on Stefano Sensi and stressed respect for referees must go both ways.
"We deserved more. I am bitter because I have seen some situations that I did not like," Conte said after the game.
"There were things that I did not like from the beginning, but I don't want to talk about that. On the bench we had some feelings I did not like.
"What did the referee tell me? Nothing, he came to warn me and he said he would send me off at the next opportunity.
"Referees have on their shirt the word 'respect' and it is the only thing I have asked. They must respect those who come here to try to do better than the other team. Respect must be mutual.
"I take away a feeling of bitterness, we are talking about a referee who led a Champions League final, a top referee who should not be influenced by Camp Nou.
"However I don't want to give the team any excuses, I'm talking about a personal feeling I had from the beginning."
The defeat for Conte's side means Inter have now lost three consecutive away matches in the Champions League for the first time, while Barcelona have extended their unbeaten run at home in the competition to 33 games.
The Catalans were helped by the return of Lionel Messi, who set up Suarez's second goal and continued his fine home form in the Champions League group stages. The Argentine has either scored or assisted in his last 13 group matches at Camp Nou.
Inter certainly could have used someone like Messi in attack with Conte left to rue his side's lack of cutting edge.
"Maybe we had to be better at capitalising on the opportunities we created, because we put a team like Barcelona in serious trouble," he said.
"In the second half they certainly pushed more, I think that for some of our players physical energy has dropped ... it is the sixth game in a few days.
"Today's defeat has been undeserved, we lick our wounds and we know we have to work to be stronger."