The Portugal international admits his side have "no margin for error" this season after seeing their lead at the top of La Liga slip away over two matches
A double from Carlos Bacca cancelled out Cristiano Ronaldo's earlier strike to condemn los Blancos to back-to-back losses, which has seen them slip to third in La Liga, three points behind leaders Atletico Madrid.
Carlo Ancelotti's side had enjoyed a 31-game unbeaten run prior to Sunday's loss to Barca, and while Pepe maintains the 4-3 defeat did not affect his side at the Ramon Sanchez Pizjuan on Wednesday, he has warned there is now no margin for error between now and the end of the season.
"I congratulate Sevilla, we tried to win but we couldn't," he told the club's official website. "There are still games left, still opportunities.
"This has nothing to do with the Clasico. They are football things. We have to be ready to win the game on Saturday against Rayo.
"We were playing well, we were pressing, but these are details. We have to be more concentrated and more determined in specific moments, and to read the game better.
"Now we have no margin for error. We have to fight knowing who is there, fighting for the league, and knowing there is no possibility for error."