The Gunners were beaten 3-1 in Barcelona on Wednesday night to fall at the round-of-16 hurdle in the Champions League for the sixth straight season.
Arsene Wenger's side also saw their hopes of becoming the first team since 1886 to win three successive FA Cups dashed as Watford defeated them at the Emirates Stadium last weekend to reach the semi-finals.
That leaves a late surge to Barclays Premier League success as the only option for Arsenal if they are to end the campaign with any silverware.
But recent form suggests that could be a struggle, given they go into Saturday's tricky trip to Everton 11 points adrift of leaders Leicester with nine games to play, having topped the table at the turn of the year.
Bellerin, however, insists the players can take heart from their display at the Nou Camp - where they showed glimpses of returning to their best.
"We can take a lot of positives and finish the season on a high," the full-back said.
"There are other things you can take from the games and now it is about focusing on the league and finishing the season on a high.
"I think we can take lots of positives because I don't think many teams can face Barcelona in the way that we did, even though the result (5-1 on aggregate) was a bit too wide given what had gone on on the pitch.
"I think we did really well and we had our chances and, while we could not materialise them, we showed we were up there."
Wenger, and to a lesser extent his players, have come in for harsh criticism from fans, former Arsenal players and pundits in recent weeks for what has been seen as a something of a capitulation - winning just two of their last nine games in all competitions.
But 20-year-old Bellerin says everyone involved with the club is still giving their all in a bid to address the current slump.
"All the players and all the staff will give everything on the pitch, but sometimes things don't go your way," he added.
"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."
On a night where Arsenal were never expected to get a result, goals from Neymar, Luis Suarez and Lionel Messi - including a wonderful volley from former Liverpool man and Gunners target Suarez - put the visitors to the sword.
But there were some positives, not least another impressive midfield display from Mohamed Elneny - whose first goal since his January move from Basle gave Arsenal brief hope.
Likewise, Wenger's decision to hand 19-year-old Alex Iwobi his first Champions League start in such a high-pressure environment also proved to be a good one as he was one of Arsenal's best attacking threats.
The highly rated winger has already been capped twice by Nigeria but admits it was 'crazy' to be involved from the start in Catalonia, with many expecting him to be farmed out on loan for the current campaign.
"It was crazy," he said.
"To play against one of the best teams in the world in one of the best stadiums in the world is a young man's dream
I was pleased because, especially at 19, I never thought I would be here playing against the likes of Messi, Neymar and Suarez
I am just happy to be here.
"I didn't know how to feel when I was told I was playing
I was buzzing
I just wanted to go out and show to the world how I could play in a match against the best in the world.
"I am pleased with my performance - I just wish that the team had won.
"I never thought I would get this far
I honestly thought I was going to go on loan at the start of the season but the manager has tried to show some faith in me and I am trying to prove him right by playing well every time I play."
Arsenal announced on Thursday afternoon that another promising youngster has signed a new deal with the club, with 19-year-old goalkeeper Ryan Huddart penning a fresh contract - the length of which was not revealed.
The England youth international was on the bench for two of Arsenal's Champions League group matches last season and has been a regular for the under-21s this term but, w ith Petr Cech, David Ospina and Matt Macey all ahead of him, he is unlikely to feature in the first team any time soon
Source : PA
Source: PA