Luis Suarez scored twice as Barcelona came from behind to beat Conte's side in its UEFA Champions League Group F encounter on Thursday (AEST).
Inter was much the better side in the first half and led thanks to an early goal from Lautaro Martinez, but Conte was unhappy with some of the decisions Slovenian Skomina gave against his side.
The 50-year-old had a number of exchanges with Skomina during the game as he vented his frustration on the touchline.
"It says respect on the referee’s shirt, so I told them that it ought to be reciprocal, that they should show respect for those who come here to play football," Conte said.
"I feel quite bitter. It pains to say it, but I saw some incidents that were directed in a certain way. There were many things I didn't like about the refereeing, right from the start.
"It is an international referee, one with a lot of experience who was in charge of the last Champions League final, so this isn't someone who ought to be influenced by the atmosphere of Camp Nou.
"It was an undeserved defeat. I don't think the result is a fair reflection of the game."
Inter, who sit top of Serie A, were unbeaten under Conte until they faced LaLiga champions Barca.
They now turn their attention to a San Siro clash with Italian champions Juventus, with Conte eager for his players to use the disappointment of this result to fire themselves up for the meeting with Maurizio Sarri's side on Sunday.
"Compliments are nice, but after a performance like that, we deserved much, much more and should've taken at least some of our chances," Conte added.
"We put Barcelona under serious pressure for long periods on their own turf, but after the break they raised the tempo and some fatigue set in with a few of our players.
"Now we lick our wounds and prepare to play Juventus on Sunday. I find it difficult to talk in positive terms after a defeat, because I suffer when we lose.
"We must realise where we can improve to not suffer the way we are at this moment, because we cannot come home happy. That is not the mentality of a great team.
"We played well, but have one point in two games. The situation in the Champions League is compromised and if we want to mature, we’ve got to return home angry."