Daniel Sturridge had put Liverpool 1-0 up but goals from Emerson and Eden Hazard put Chelsea into the next round.
Shaqiri had the opportunity to seal victory for the Merseysiders moments before Hazard struck but spurned the chance.
And after the final whistle, Klopp seemed to explode at his summer signing with images of the German shouting at Shaqiri doing the rounds on social media.
But Klopp has denied suggestions that the pair were arguing and revealed what he told the Switzerland international.
“I spoke about a free-kick, the last one,” Klopp said.
“We wanted to have Mo (Salah) a bit wider, so we had passed the ball to Mo, the whole bunch of players was in one direction – where we shot the ball, actually.
“But if we can send Mo into a one-on-one situation in the last situation of the game, it would have been not too bad.
“What I said was about the free-kick, nothing else.”
Klopp picked a much changed line-up with the likes of Roberto Firmino and Salah starting on the bench.
But the manager is not expecting many to keep their place when Liverpool face Chelsea again on Saturday, this time in the Premier League.
“Let me say it like this: hopefully they don’t have to (retain their place),” Klopp added.
“It was very intense. A few of the players who were not involved tonight are not 100 per cent fit, so we will see what we do.
“But it would be cool if we could make these changes again because not playing for a long time and then playing these 95, 96, 97 minutes and then playing three days later again would, of course, not be pure joy.
“We have to see. But they did well, that’s good.”