The Reds blew a 2-0 lead at New Meadow to ensure they would play a fourth-round replay at Anfield on February 4.
"We are really disappointed obviously because we could have done much better than our performance tonight," Adrian told Liverpoolfc.com.
"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.
"Now we have to face the second game in Anfield to try to go through to the next round.
"They deserve all the respect we give them. We respect all the rivals obviously but when we are on the pitch it's 11 against 11, so you give everything for the result.
"At the end, they got a draw and obviously it's like a win for them because we have to play the second game now at Anfield.
"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."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!