Liverpool's comfortable 3-0 win has underlined their credentials as they aim to win a first championship since 1990, and afterwards captain Steven Gerrard insisted they are genuine contenders.
Liverpool are just four points behind leaders Chelsea with a match in hand, lead Arsenal on goal difference and are two points in front of Manchester City, although Manuel Pellegrini's side have two games in hand.
"I think they are going to be worried," said the Liverpool full-back.
"We put a marker down (at Old Trafford). I think we are ready to push on and keep going.
"We all believe but our priority was top four at the start of the season. We are on track for that and anything else is a bonus.
"It's always good when you see other teams around us getting beat. We saw the Chelsea result (losing at Aston Villa on Saturday) but we just concentrate on ourselves.
"We are just taking it a game at a time and keeping our feet on the ground."
Liverpool's defence have now had back-to-back clean sheets after conceding in five games in a row and Flanagan puts that down to their efforts on the training pitch at Melwood.
"All the lads are working hard," added Flanagan.
"We have had a bit of criticism about our back four lately but we have been working hard in training and keeping it tight.
"To keep clean sheets has been great for us and hopefully we can keep many more.
"It's not just the back four, it's the whole team working hard in defending as well, so the manager has been working hard and we are just trying to put that in our game."