The Russian team were surprise winners at the Sanchez Pizjuan on Tuesday but well worth their 2-1 victory on the night, which put them in the quarter-finals 3-2 on aggregate.
Sevilla left the pitch to whistles and chants for Jimenez to go from some sections of the home crowd, who have been unhappy for some time at what they believe are his conservative tactics.
"Of course it hurts. Now, it will be said it was the whole stadium, though it clearly wasn't," Jimenez told an increasingly tetchy news conference after the match.
"I'm the only person responsible for what has happened. CSKA are a very good team even though they don't have the name of other sides, and have waited for their chances and made the most of them."
Sevilla lie fourth in La Liga, 21 points adrift of leaders Real Madrid, and are in the King's Cup final, but club president Jose Maria del Nido fell short of giving Jimenez a ringing endorsement.
"All I can say is that Jimenez will be coach until the end of the season," he told Spanish state television.
"We can't win the league so we have to concentrate on claiming third or fourth place and on winning the Cup."
