Runaway Premier League leaders Liverpool looked to be heading into the fifth round for the first time since 2015 after a fine first-half finish by 18-year-old Curtis Jones was followed by Donald Love's own goal in the opening minute of the second half.
Klopp said, "It's difficult to win the game. We don't have enough time to say all the things which weren't right today.
"We scored a really good goal but apart from that, Adrian had absolutely too much to do. He was brilliant. The counter-attacks they had when we lost the ball...
"They slowed the game down in their formation and we lost the ball in the wrong moments. It just didn't look like it was 2-0 [to Liverpool] on the pitch. It looked like we were 2-1 down.
"But well deserved for Shrewsbury, it was the minimum they deserved. Congratulations to them."