The Catalan giants were particularly wasteful in the first half at Estadio de los Juegos Mediterraneos, with Lionel Messi missing an open goal from close range, and Almeria capitalised through Thievy Bifouma.
Congo international Thievy produced a fine finish after latching on to Fernando Soriano's throughball, with Barca left staring at a third successive La Liga defeat, a run they have not suffered since 2003.
However, after the introduction of Neymar and Luis Suarez at half-time, Barca produced an improvement, with the two combining for the Brazilian's equaliser.
Jordi Alba claimed victory in the final 10 minutes as he steered home Suarez's cross, but Luis Enrique does not want the win to paper over the team's problems.
He explained: "We could not counteract Almeria at first, but then we scored on the counter. That heightened our mood. It wasn't a great game, but with attitude and desire of the players, we came back
"[Almeria] didn't surprise me. We knew we'd leave spaces out wide and that they'd both play strategically and on the break.
"The game was complicated, but the substitutes, not the performance, won us the game. Sometimes this can happen, but it mustn't paper over what we did wrong.
"I prefer to assess the team. Individuals are less important. We have to improve our game and win more points and games to make up the ground [at the top]. That's the goal.
"It's simple. To be successful, you have to win when you play badly, like today. The best thing [about today] was the result."
