Ronald Koeman's side went into the game without the services of Messi, who was granted an extended holiday break by the Dutch manager earlier in the week to deal with an ankle issue.
Barca had the chance to take the lead inside of 15 minutes after VAR awarded them a penalty, but Martin Braithwaite skewed his spot kick wide of the goal and match remained scoreless.
The hosts dominated possession, but it was Eibar that had the better of the chances as Barcelona keeper Marc-Andre ter Stegen made two solid saves to keep the scoreline at 0-0 going into half-time.
Barcelona came firing out of the gates in the second half, with an enlivened attack leading to a pair of near misses from Ousmane Dembele and Miralem Pjanic in the opening five minutes after the restart.
Koeman said: "We deserved to win, we did enough. They had one shot on target. We made chances, but we didn't score the penalty and then we make a mistake in defence.
"We did well, we worked hard and did enough to win but this is happening to us a lot. In the first half, we had problems bringing the ball out from the back, we didn't fine players between the lines.
"Maybe it was the fear of taking the risk. But once again, a game where we create a lot but don't take our chances."
Philippe Coutinho limped off in the closing minutes with an apparent injury as Barca pushed for the winner, but none came as Eibar picked up their first point at the Camp Nou in the seven matches they've played there.
Following the match, the 21-year-old Araujo took full responsibility for his costly error.
"It's a mistake from me, one I can't afford to make," Araujo told reporters. "It was a lack of concentration from me and these are mistakes we cannot afford to make.
"Today it was my personal mistake, I'm old enough to know how big a responsibility it is to play for Barcelona.
"It's a shame for us we weren't able to get the three points as we needed and wanted them."
The draw means Barca have dropped nine out of 27 possible points at home this season and are now in sixth in the standings on 25 points from 15 games, seven behind Liga leaders Atletico Madrid who have two games in hand.
And Koeman admitted after the match, winning La Liga would be a massive challenge.
"If I am realistic, winning the league is really complicated," Koeman said. "Nothing is impossible, but we have to recognise the distance between us and the leaders. Atletico look really good to me, strong, not conceding many goals."