Liverpool missed the chance to go back to the top of the Premier League, when they were held to a 0-0 draw at neighbours Everton on Sunday.
Mohamed Salah and Fabinho missed the best chances to win it, but the draw means Liverpool are now one point behind Manchester City with nine games to go.
Liverpool had the better of the chances at Goodison Park, with Salah missing a couple of times and Fabinho mis-controlling in front of goal.
Defender Virgil van Dijk said Liverpool deserved the three points.
"It says a lot that they are celebrating a 0-0," he said. "We had chances to win the game and did not finish them off.
"It is what it is. We go again.
"We focus on our next game, everyone wants to be top of the league and we cannot change the situation at the moment."
Liverpool captain Jordan Henderson said they needed to be more clinical in front of goal.
"We created enough chances. We've just to stay confident, keep going and see where it takes us."
Brendan Rodgers tasted defeat in his first game as Leicester manager, when Andre Gray's injury-time winner gave Watford a 2-1 victory.
Jamie Vardy looked to have secured a point, when he equalised Troy Deeney's early header, but Gray scored from close range two minutes into time added to win it for the home side.
Watford remain eighth, though level on points with seventh-placed Wolves, while Leicester stayed 11th.
"I thought, after going behind so early, we regrouped and had some good moments," Rodgers said.
"At half-time, we reinforced about some issues around the speed of our game, but I thought the play was excellent.
"It looked like only one team would win the game. The goal at the end is a case of managing the game.
"It is something that will get better, as we work together. I was pleased with the spirit of the team."
Watford had been humbled 5-0 at Liverpool midweek, but Deeney headed Gerard Deulofeu's teasing free-kick into the Leicester net for the opener after just over four minutes, the 12th goal Leicester have conceded in the first 15 minutes this season.
"Based on possession and keeping the ball Leicester deserved [more]," Deeney said.
"But we were more potent, especially in the first half. We are a threat going forward, we always look like we will score.
"We aren't happy to win just one and lose three, we want to finish as high as we can."
Caretaker manager Scott Parker took charge of Fulham for the first time and saw his team fight hard, but eventually fall to West London neighbours Chelsea.
Gonzalo Higuain put Chelsea in front on 20 minutes, only for Calum Chambers equalised seven minutes later, but Jorginho netted the winner four minutes after that.
Chelsea manager Maurizio Sarri praised his side, although he admitted they had tired as the match went on.
"In seven days, we played 120 minutes in a difficult match against City, we played 90 very expensive minutes against Tottenham and today, a very important derby against a team with a new coach," he said.
"It was a very difficult match - very good for 60 minutes, then very tired, but it was a normal reaction to our seven days."
Parker's side are now 10 points short of safety with nine games to play.