The Reds' top-four hopes were damaged by the loss of a late winner by Crysencio Summerville.
The hosts had lost to bottom-of-the-tableNottingham Forest in their last league outing but were hoping to pick up where they left off in the group stage of the competition.
The worst possible start for them was when a poor back pass by Joe Gomez led to a goal by Rodrigo.
The Reds responded well and were able to tie it up soon after.
Even though they were lying in the bottom of the table, they showed great hunger and desire and hit the woodwork.
Illan Meslier made a number of saves in the second half, including denying Darwin Nunez one-on-one.
In the final minute of the game, Summerville picked up the ball and fired across Alisson to send the away support into a frenzy.
The loss means that they are ninth and eight points off the top four.
There's more to come.