However, Monk has revealed that he has "no complaints" with how his team performed at Anfield, insisting that they only lacked "composure and luck".
The 37-year-old is quoted by BBC Sport as saying: "I think what was missing was that bit of composure and luck.
"I can't have any complaints apart from the result. I told the players that I was gutted for them. We want to try and make this a regular fixture and if we can keep focused on what we're doing then hopefully we can be successful."
Leeds will now return to league action as they look to build on fifth position in the standings.