Jurgen Klopp says Liverpool's defenders were partly to blame for the error from Adrian that ensured a nervy final few minutes for the Reds in the 2-1 victory over Southampton at St Mary's.
After a slow start in the first half, a stunning strike from Sadio Mane gave the visitors the lead just before the break.
Mane then teed up Roberto Firmino to make it 2-0 in the second half, but with Liverpool well on top they shot themselves in the foot when stand-in keeper Adrian passed the ball straight to Danny Ings, who fired home.
Ex-Reds forward Ings then missed a glorious chance to make it 2-2 late on, but Klopp wasn't blaming Adrian - who survived an injury scare to play in the game having recovered from the ankle knock he picked up when a celebrating supporter ran into him in the aftermath of the European Super Cup win on Wednesday.
With No.1 Alisson expected to be out for at least another month with a calf injury, there were suggestions that 35-year-old Andy Lonergan might be needed to start the game for Liverpool, but the veteran stopper was only on the bench.
And Klopp - who joked that Adrian was copying Alisson's blunder in the 2-1 victory over Leicester City early last season - said his defenders put the former West Ham keeper under too much pressure.
"Adrian had a swollen ankle, so we played too many balls back to him," he said.
"I was happy with everything he did today, all the saves, all that stuff. The other players have to feel more the responsibility for the build up.
"You can’t give all the balls back to him and hope the painkillers are working."
The win was Liverpool's second in their two Premier League games this season, with midfielder Alex Oxlade-Chamberlain playing for 89 minutes in what was his first Premier League start for 16 months.
"The main thing is the three points for the team, whether I'm on the pitch or not," he told BBC Sport afterwards.
"But on a personal level it is great to be back out there and contributing to a good solid performance.
"That's what you miss. I've been working hard to get back to this point, I've had iffy moments along the way, but I have to keep reminding myself it is a long journey back to where I want to be."
