The Whites were on top for the first hour and created the better chances, hitting the post through Kemar Roofe before the Reds' Ben Woodburn grabbed all the headlines with an emphatic 81st-minute finish.
Divock Origi's second strike in as many matches had broken the deadlock in the 76th minute at Anfield.
"The team can be proud of what they did," Monk said. "With a little bit more composure, we would have scored two or three goals.
"Unfortunately their quality came through at the end and they scored the goals.
"We deserved more, if we carry on like that we can be successful. The ambition now is to have these types of games week in, week out."