The Gunners travelled to the Spanish city with a 2-0 deficit from the first leg, and despite Mohamed Elneny scoring his first goal for the club to equalise on the night, Bellerin's side were blown away by the brilliance of Barca's front three.
Goals from Neymar, Luis Suarez, and Lionel Messi consigned the visitors to a 5-1 defeat on aggregate to end Arsenal's hopes of European glory for another year.
However, despite the defeat Bellerin is adamant that the return leg should only have made himself and his teammates more confident after a gutsy and encouraging performance.
He said, as quoted by the Express: "I think we can take lots of positives because I don’t think many teams can face Barcelona in the way that we did. I think we did really well and we had our chances and while we could not materialise them, we showed we were up there.
"The team did really well on the pitch and I don’t think many teams have created as many chances against Barcelona as we did. We have to be a bit more efficient in front of goal, the way they are, and for us we need to keep our heads up and take the positives of the game.
"All the players and all the staff will give everything on the pitch but sometimes things don’t go your way. You need to focus on where you want to get. That is football. Sometimes you are high, sometimes you are low. It is about being high as much as we can and hopefully things will get better."
Arsenal now look almost certain to finish the season without a trophy, having been knocked out of the FA Cup by Watford last weekend.
The Gunners are 11 points behind leaders Leicester City in the Premier League table, albeit with a game in hand, after a run of just two wins in their last nine league matches.