Rooney could not hide his dismay following the game, during which Steven Gerrard netted two penalties for the visitors before Luis Suarez scored late on.
The 28-year-old told MUTV: "It's one of the worst days I've ever had in football.
"It's hard to take. You have to give Liverpool credit - they played well - but it's difficult to take.
"Nobody wants to lose, especially in this way, in your own stadium. It's not nice."
As for the match itself, he added: "To go behind by one penalty was hard to take.
"We had a game plan for the second half, which went out the window when they got the second penalty so early on.
"It made it an uphill battle to come back. I thought after that we had a couple of chances where I thought, if we got one, we could have gone for a second and maybe we could have done it.
"I haven't seen the penalties back again but from where I was standing on the pitch I don't think we can argue with them."
United's season will be effectively ended if they fail to overturn a two-goal deficit in Wednesday's Champions League clash at Old Trafford against Olympiakos who won the first leg 2-0.