The 27-year-old made it clear at that time he would not be requesting to miss the fixture in Belgrade, while Klopp said he would consider the matter in the coming days.
Milan Pavkov scored both goals as the Group C's basement club picked up their first win of the competition to give themselves hope of continuing in Europe.
Liverpool had the briefest of openings, but, uncharacteristically, Adam Lallana's first touch let him down as he tried to control Salah's square pass inside the penalty area.
You may think I have lost my mind after last night's tepid performance against Red Star Belgrade but their side is still packed full of quality and they still have the experience of last year's run to the final.
"We scored at the right times at Anfield but they are a different beast at home and they proved that against Napoli when they got a draw here", he told a news conference.
Adam Lallana nearly got Liverpool back in the game moments later but his header was deflected just wide, and Sturridge then fired wide from just inside the box. We want the focus to be on a great game of football, free from anything else.
"We knew [about the atmosphere]", he said.
Klopp regularly conducts analysis with his players the day after a game, having reviewed the match himself at least twice but Wednesday's debrief assumed a more critical air given the nature of defeat and the precariousness of Liverpool's position in the group.
"I think it's one of those periods we need to get through", added the Scotland captain.
BATE have managed just two wins in their last 15 Europa League games (D5 L8), scoring 13 goals and conceding 33. "We have to make sure in Paris that we do better".
"We get extra energy from the stands, and although this may not have much impact on the Liverpool players, I believe that this will be a fascinating atmosphere for them".
'The manager kept saying we need to finish first in the group, and the earlier the better so tonight we've done the job even if we could have been more efficient, ' he said.
"Napoli came here and found it tough as well, so it's a tough place to come, but we expected that".