Brendan Rodgers believes Manchester City's faltering title challenge will serve as a warning against complacency to Liverpool when they take their pursuit of the Premier League to struggling Norwich City on Sunday.

Liverpool's prospects of a first title win since 1990 were enhanced on Wednesday when the club with the biggest wage bill in world sport were held to a 2-2 draw at home by bottom-of-the-table Sunderland. The result left City six points adrift of the league leaders having played one game fewer. On the same night Rodgers watched Crystal Palace damage Everton's Champions League aspirations with a 3-2 win at Goodison Park that effectively secured their Premier League status.

Both results shaped the Liverpool manager's address to his squad at Melwood on Thursday. "I said to the players before we started training this morning that if there was doubt about our rivals dropping points, then they should also take last night's results as a warning sign," he said.

"It was a warning sign for everyone that, at this point of the season with four games to go, there is nothing guaranteed and I have said that all the way along. Crystal Palace had an excellent result and Sunderland were within minutes of getting a great victory. That was the biggest message I got from last night. Yes, one of our rivals might have dropped points but that is irrelevant. You have to do your own job. The warning signs are there."

Norwich are fourth bottom and two points clear of Fulham ahead of Neil Adams' first game as manager at Carrow Road since replacing the sacked Chris Hughton last week. Their recent record against Liverpool is woeful, having lost the past four league meetings by an aggregate score of 18-3 and been on the receiving end of two hat-tricks plus a four-goal haul from Luis Suárez in that sequence. As evidenced by Sunderland and Palace, however, Rodgers believes Premier League survival will spur Norwich on Sunday.

"When you're so close to the finishing line you can maybe think that the job can be done and is done," he said. "Teams can look that they are playing teams towards the bottom of the league and that those games might be easy, but actually it's the contrast – they can be even more difficult. People are fighting for their livelihoods, fighting for their lives, fighting for their children, fighting for the supporters. And they're fighting to play in the best league in the world. That is the nuts and bolts of it."

Liverpool's biggest threat for the title now comes from José Mourinho's Chelsea, who visit Anfield a week on Sunday, but Rodgers insists the potential Premier League decider has not entered his thoughts. He insisted: "We haven't even thought about Chelsea. We've been brilliant in the big games this season – Man United, Tottenham, Arsenal, Man City – but it is about Norwich and that's it."

The Liverpool manager also dismissed suggestions that last Sunday's victory over City at an emotion-charged Anfield, where the 25th anniversary of Hillsborough was commemorated before the game and his team survived a second-half recovery to win 3-2, could take a psychological toll on his players. "We are into the final block of games and that was just another one ticked off. We really only focus on the next game," he said.

"It is never easy at this stage. We have to stay calm and focus on what we want to achieve. Our determination is there, our fitness is there, you look at the intensity of the work of the team last week and it was phenomenal really. All the young players coped with the pressure and the older ones helped to get the team through. There certainly won't be complacency or nerves. There won't be pressure on us. It is the same demand as for every game: which is to play well and win.

"For the first 45 minutes last weekend we were unplayable and that was against a top group of players who have scored a lot of goals and have some world-class players. It was 20 minutes from City at the beginning of the second half where we had to stand up and be counted. When you have the biggest wage bill in sport you have to perform at some stage in the game. Then we came back and showed what great teams do, we showed resilience and quality. There have been a lot of questions about the team and we have come out with all the solutions.

"We certainly don't have our hands up in the air. The finishing line is a wee bit out, we just need to focus and keep producing the performances that we have."

Liverpool will be without the suspended Jordan Henderson at Carrow Road while Daniel Sturridge is a doubt for the game due to a slight hamstring strain. Rodgers said: "It's not too serious, it's not going to keep him out for too many weeks, but he may be a risk for the weekend. We'll assess it more over the next couple of days. Fortunately Daniel recovers very quickly."