Sturridge was handed a piece of paper by Klopp in the second half of Liverpool's 1-0 first-leg defeat on Wednesday, before the forward was seen offering instructions to his team-mates following Nathan Redmond's 20th-minute opener.
Klopp revealed the contents of the note post-match, the German manager telling reporters: "New system. Whatever we want to call it, 3-5-2. Lucas [Leiva] at the back, Emre [Can] in the centre, two wingers, two strikers. Half space for [Adam] Lallana and [Philippe] Coutinho.
"That's all. No more information but it was enough. Maybe it was a little bit too late.
"We gave the paper when the game was already running again, that was our mistake.
"I would say seven or eight [of my players] knew immediately. Roberto [Firmino] needed a little longer [to understand]. But he was close enough to us. Things like this happen.
"That's not about being frustrated. That's about thinking you have chance, that's all. What type of guy would I be if I sit outside, if we play well, I think I'm a wonderful manager, that's not like this, we tried to help.
"We thought it makes sense to have real wingers, high, make it more difficult for them to defend the wing, to have to play someone in the centre, Phil and Adam. Two strikers. Roberto with Daniel. That's all, it's not because we're frustrated."