A 3-0 victory at Manchester United on Sunday underlined their credentials to make a bid for a first championship since 1990, and afterwards captain Steven Gerrard insisted they are genuine contenders.
Liverpool are four points behind leaders Chelsea with a match in hand, ahead of Arsenal on goal difference and two points in front of Manchester City, although Manuel Pellegrini's side have played two matches fewer.
"I think they are going to be worried," said Flanagan.
"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 has come in for criticism recently but have now had back-to-back clean sheets after conceding for five games in a row.
"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."
Manager Brendan Rodgers insists he has not banned his players from talking about a possible bid for the title.
Rodgers has long played down the likelihood of his side winning a first league championship since 1990 and does not intend to start promoting their chances now, although he is happy for his players to use it for inspiration.
"I've not banned it (talk of the title). We have better things to talk about," he said.
"It is about improving and getting better. I don't lose sleep over it.
"We are up there on merit so of course we have an opportunity. I didn't say [we have] no chance. If you think we have a chance then write it.
"I try to not expect so much and let the players do the talking. We try to remain dignified in our work and our players are doing all the talking.
"We will focus on the next game against Cardiff. I think other teams will drop points - we may well drop points, we may not - but I can only look at our next game and I've done that since I walked through the door, and I'm not going to change."
Liverpool recorded their first victory at Old Trafford since 2009 and only their 16th league win on the ground in 118 years thanks to two Gerrard penalties and a late third from Luis Suarez.
"We've showed that we are genuine contenders and we are going to fight to the end for this," Gerrard said.
"We believe it but I've said many times that in football the easiest thing to do is talk the talk.
"We've got to go and treat Cardiff like Manchester United and we've got to treat Sunderland like Manchester United.
"If we do we will win a lot of games until the end of the season. The rest of the teams around us have to believe we're going for it."