Kolo Toure admitted Liverpool's defeat by Manchester United was 'hard to take' but the defender has not given up hope of a top-four finish yet.

Jürgen Klopp's side were the dominant force in Sunday's encounter with their bitter rivals, creating a string of good chances only to be let down by wayward finishing or denied by opposition goalkeeper David de Gea.

And that set United up to land a sucker-punch in the 78th minute when the ball fell to Wayne Rooney in the box and he smashed home to clinch the victory.

Unsurprisingly, the nature of the defeat made for a low mood in the home dressing room, according to Toure.

"We feel really down, to be honest, because it was a game that we dominated, we played very, very well, we were strong at the back," he told Liverpoolfc.com.

"But at the end the set-piece changed everything. We were the better team and the better team lost.

"We were the better team, we played well, created some chances, but at the end we lost. This is really hard to take."

But, while the result leaves the Reds six points adrift of Louis van Gaal's team and some way short of the Champions League qualification places, Toure has not yet given up hope of closing the gap during an unpredictable Barclays Premier League season.

He added: "This league is crazy. Anything can happen. We just need to carry on putting in that kind of performance."

One aspect Toure acknowledges Liverpool need to improve on before they plot a course for the upper reaches of the table, however, is set-piece defending.

"We need to organise better," the Ivorian said.

"Rooney was at the back on his own to score his goal and it's very frustrating. I feel down, like all the team, but that's football. 

"Sometimes you play well and lose, sometimes you play not so good and you win. We need to carry on playing and focusing to avoid that kind of situation."