"We've showed that we are genuine contenders and we are going to fight to the end for this. We believe that we can win the league," he said after Sunday's 3-0 win at Old Trafford that sees the Reds move up to second place.
"I have come here many times before and been played off the park. They are a fantastic team and this is one of the most difficult places to come in the Premier League.
"We've come here and dominated from start to finish, yet we're still going away slightly disappointed that we didn't score more goals.
"It was one of the most comprehensive away performances at Old Trafford for many years. Liverpool absolutely battered them in all areas and United looked like strangers.
"Make no bones about it, it could have been six or seven, Liverpool's movement was so good. Liverpool were on the front foot and United were nowhere near it.
"We will enjoy this, but we'll need to move on quickly. The easiest thing in football is to talk the talk.
"We have to treat Cardiff and Sunderland the same as Manchester United."