Sergio Busquets conceded that Barcelona's hopes of winning La Liga evaporated with Tuesday's 3-3 draw against Levante.
Barca led 2-0 and 3-2 in Valencia before conceding a late equaliser to leave their title hopes hanging by a thread after picking up just five points from their last four games.
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In addition to winning their remaining two fixtures, Barca need Atletico to drop at least five points from their final three matches and Real Madrid to lose one or draw two of their last three games.
"We don't have much of a chance now," Busquets told Movistar after the final whistle at the Ciutat de Valencia stadium. "It will depend on our rivals, but this is our own fault, [bad] decisions, a lack of concentration. We concede goals too easily.
"We don't feel good because it was always going to be difficult, but we wanted to put pressure on those at the top. We had the lead, but as has happened this season, [Levante] scored goals too easily. The point doesn't mean much because that's the league practically over for us. We've dropped too many points to fight for the title."
Atletico can open a four-point lead over Barca with just two games to go if they beat Real Sociedad on Wednesday. Real Madrid, meanwhile, can move two points clear of the Blaugrana if they win at Granada on Thursday.
Barca's chances are further hindered by the fact both Atletico and Madrid have the superior head-to-head record against them, which is the determining factor should two teams finish level on points after 38 games.
The draw with Levante brought further questions about coach Ronald Koeman's future at the club.
Sources told ESPN earlier this week that there are doubts about the Dutchman's long-term suitability to the role, regardless of whether or not Barca go on to win the title to add to their Copa del Rey success earlier in the campaign.
However, a failure to claim top spot this season, given Barca had their fate in their own hands before the defeat to Granada on April 29, could accelerate calls for him to go.
"There are always questions about coaches, that won't change," Koeman said in a news conference when asked about his job prospects. "But after that second half, I understand there will be questions, of course."
Lionel Messi's 29th league goal of the season and Pedri had helped Barca into a two-goal half-time lead but quick-fire goals after the break from Gonzalo Melero and Jose Luis Morales drew the hosts level.
Ousmane Dembele restored Barca's lead in the 64th minute but a late goal from Sergio Leon earned Levante a point.
"Sometimes it's difficult to explain [what happened]," Koeman added when asked what went wrong. "Analysing the game, in the first half we were good, there was a good rhythm with the ball, good intensity. We created chances to score and we went in 2-0 up.
"At the start of the second half, we lost the ball more, our intensity dropped and we switched off defensively. It's difficult to reverse that once you've let them back into the game, as we did [by conceding] three goals in 35 minutes."