Liverpool manager Brendan Rodgers bemoaned his side's below-par first-half performance as they fell to a crushing 2-1 defeat to arch-rivals Manchester United on Sunday.

Daniel Sturridge's 69th minute goal was not enough to rescue the Reds a result after two fine goals from Juan Mata gave Louis van Gaal's side a deserved lead at Anfield.

Rodgers saw skipper Steven Gerrard sent off for a vicious stamp just 40 seconds after coming on as a substitute at half-time and 10-men Liverpool fell five points behind 4th spot with the loss, but the Northern Irishman believes their first-half showing gave the visitors the advantage.

"It was a game where the first half cost us more than the second," said the Reds boss.

"In the first half, the game was set up to press the opponent high up the pitch, but our starting position was way too deep, and we handed over control way too easy. They were able to circulate the ball well, and we were never in position to press well enough.

|In the second half, the players showed why they’ve been on the run we’ve had, their great character and resilience. They were still in the game right to the end, and the message at the end was that I take great pride in that."

When asked what went wrong for his side, Rodgers replied: "It was simpler than the system. They were playing 4-3-3, but we were too deep on the sides at first. The idea was to be 15 to 20 metres higher up the field, and that would have given us more numbers to press the game.

"It was only in the last 15 minutes of the first half, where I had to manufacture the team into a diamond, that we pressed. That forces the players to be closer and get higher up the field. We made a better game of it.

"Across our game, with and without the ball, we weren’t at a high enough level. And particularly for a game here, that disappoints.

"In that system, you have to be able to press well and pass well. And if it’s not, then it becomes much more difficult to be effective. That’s how it was in the first half, we didn’t pass it anywhere near well enough, and we didn’t press, so both sides of our game suffered.

"We just didn’t play well enough. You have to accept that. It wasn’t our day."

Liverpool have a timely international break to gather themselves before another monumental clash against top-four challengers Arsenal, who currently sit third.

Whilst the Reds' hopes were severely dented on Merseyside by United, Rodgers insists all hope is not lost with a further eight Premier League games remaining.

"It’s a big challenge, but when I looked at the last 10 games, it was always going to be difficult to win all 10," Rodgers said. "So I built in a loss and maybe some draws.

"We hoped it wouldn’t be in this game, against a rival, but it (top four) is still very much possible. It’s five points, and we have now got to recover and use it as the same springboard that we did in the last game.

"They played well, deserved the win, and we will go away and recover and look to go again and get a victory in our next game, which we have shown we are more than capable of."