Adrian admits Liverpool have only themselves to blame for the surprise FA Cup setback that has prompted fury.
The Reds threw away a 2-0 lead to draw 2-2 at League One side Shrewsbury Town in their fourth round tie on Sunday.
Liverpool boss Jurgen Klopp has subsequently sparked heated debate after he revealed he would "respect" the Premier League's international break by vowing to not play any senior players in the replay with under-23s boss Neil Critchley slated to be in charge if the game takes place, as expected, next midweek.
But Adrian, who made some important saves, believes Liverpool should have avoided that situation in the first place.
"We are really disappointed obviously because we could have done much better than our performance tonight," said the goalkeeper.
"The result at the end was fair but the penalty they got was outside the box. But they had also many chances, they had many one-v-ones and we could have defended much better than we did.
"They deserve all the respect we give them. But we need to have a look at ourselves and criticise ourselves because we are most critical of ourselves and try to improve and keep doing like we are doing in the Premier League."
Adrian admits Liverpool decreased their intensity once Donald Love's disastrous own goal put them two ahead shortly after the interval.
"It’s true in football that you can never play relaxed," he said, speaking to liverpoolfc.com."I think we relaxed a little bit after our second goal and after that they pushed even harder.
"They had desire and they tried to score. Then we conceded the first goal and then obviously the second one got us a bit down."
