The Catalan giants have won three consecutive league games for the first time this season.
Doubles from Lionel Messi and Antoine Griezmann at the Nuevo Estadio de Los Cármenes made sure Koeman’s men have won four consecutive away games.
Speaking to the media after the game, Koeman insisted that winning titles depends on the team’s mentality and admits he remains confident after Barcelona’s performances against Athletic Bilbao and Granada this week.
"[Winning titles] doesn't depend on just one player," the former Everton head coach told Marca.
"It depends on the mentality of the team. If everyone is well and in their best form, they can fight [for titles]. With the gap to the leaders, it'll be difficult, but this week we have played well which gives me confidence.
Messi put up yet again another masterclass as his first half brace helped sink Diego Martinez’s charges.
"Barcelona need Leo," Koeman added.
"Because of his importance and effectiveness. We need him to fight for titles. "Thanks to the lead we were able to take him off. Messi tries his best for the team and lately he has been doing very well, very effective.
"Like the rest of the team, the start of the season was poor, but he has always been motivated. Now he is scoring more, but he has always been involved.
The victory has moved Barcelona to third on the league table, four points behind Atletico Madrid who sit first with three games in hand.