Liverpool manager Brendan Rodgers said he had Arsenal and Manchester United in his sights after his team closed on the Champions League places with a 2-0 success at Southampton.

A glorious 30-yard strike by Philippe Coutinho put Liverpool ahead in the third minute of Sunday's game at St Mary's and after a number of vain Southampton penalty appeals, Raheem Sterling sealed victory late on.

Liverpool play second-place Manchester City next weekend before tackling fourth-place United and third-place Arsenal over the next six weeks, and Rodgers is confident they can close the two-point gap separating them from the Premier League's top four.

Asked if he was apprehensive about Liverpool's fixture list, which also includes a trip to Besiktas in the Europa League on Thursday, Rodgers replied: "Not at all.

"We might have been at the beginning of the season because of how we were playing. But when the team's in the condition it has been for these last two and a half, three months, then we relish every game we play.

"We have Man City and Man United at home, Arsenal away. For us it was a big step today (Sunday), considering the start we've had to the season. It really shows the consistency the players are at."

While there was much for Rodgers to savour in Liverpool's smash-and-grab win, he was dismayed by the reception afforded to his former Southampton players Adam Lallana and Rickie Lambert, who moved to Anfield last year.

Although Lambert was granted a warm reception by the home fans, Lallana was roundly jeered, and Rodgers was also disappointed that neither player received a tribute in the match-day programme.

"I'm a wee bit disappointed for Adam, I've got to say," said the Northern Irishman, whose side have gone 10 league games without defeat.

"Adam was captain here for two years and gave an incredible service to Southampton and I know for a fact he could have left here a number of times, and didn't. And to get the reception he got was disappointing.

"I looked in the match programme and there was nothing relevant to his time here and all the time that he's been here since he was a boy.

"And the likes of Rickie Lambert, great servants to here, incredible players who got the club to where it is today, and there was no mention of them, which I thought was sad."

Filip Djuricic, making his first Southampton start, had penalty appeals waved away by referee Kevin Friend either side of Coutinho's goal and manager Ronald Koeman felt that the second, when the on-loan Serbian forward appeared to be felled by Joe Allen, merited a spot-kick.

Southampton were also aggrieved when Simon Mignolet raced out of his box to repel an attempted lob by Eljero Elia shortly before half-time, in an incident that saw the ball strike the Liverpool goalkeeper on the chest before bouncing up and hitting his arm.

"The situation of Elia, hands or no hands of the goalkeeper, it's difficult to see," said Koeman, whose side remain fifth, a point above Liverpool.

"I can understand the decision of the referee, but I don't understand the second situation in the game (Allen's challenge on Djuricic) because that's a clear penalty.

"But I'm proud of how the team played today. We know in the last few games we've struggled with scoring goals.

"If you play three times in a row and don't score (at home), it's difficult to win games, but that's part of football."

Koeman also revealed that Senegalese forward Sadio Mane had started the game on the bench because he had reported late for the team's pre-match meal.

"Everybody can be late one day, in the morning," the Dutchman said. "But you can't be late at one o'clock when you have to play against Liverpool."