Soccer:Manchester City manager Roberto Mancini had a woeful night at Anfield as his side lost 3-0 to Liverpool and captain and top scorer Carlos Tevez limped off with a hamstring injury which will almost certainly keep him out of the weekend's FA Cup semi-final.

The Italian accepted full responsibility for the defeat, which damaged their Champions League aspirations, admitting he had made a "mistake".

The visitors were off the pace from the start and trailed 3-0 at half-time to two goals from Andy Carroll, his first for the club since his €40 million January transfer from Newcastle, either side of one for Dirk Kuyt.

Their problems increased as Tevez's expected absence at Wembley will be a major blow as City seek to end their 35-year wait for a major trophy.

"Carlos has a hamstring injury, it will be very difficult for the semi-final," said Mancini of the Argentina striker's injury.

"I don't think he will play. We will try to recover him but it is very difficult because we also have to think about the other six games for Champions League (qualification)."

However, it was the Italian's slightly mysterious admission of unnamed errors in his preparation in the days prior which posed more questions than answers.

"I am disappointed with myself. I made the mistake for this game not with the players, the players played 100 per cent, it was my fault" said the City boss, who refused to say what his mistake was.

"I made a mistake in the last two days, I know why. It is important I understand this for the next game. It was my mistake because we did not prepare very well. I made three changes, bringing in three fresh players, our focus was not good.

"Liverpool played fantastically in the first 20 minutes, we left a lot of space for them, and they were very aggressive at the start and we played very soft. After 20 minutes we started to play but it was late. For this it is my fault, it is important for me to understand this."

Carroll grabbed the headlines after breaking his duck in his sixth match, having been delayed by injury, since joining from Newcastle.

Manager Kenny Dalglish had always insisted there was no pressure on the England international to start justifying his transfer fee, and he suggested at the weekend the time to judge Carroll and partner Luis Suarez would be in 12 months' time.

"It is great to see the big man get off the mark," he said. "The first one was a fantastic strike, the second a good header.

"You can see the more Andy and Luis play together the better the understanding is and I thought Luis played outstandingly tonight and was unfortunate not to open the scoring when he hit the post.

"It was a fantastic performance. I think they thoroughly deserved the 3-0 victory. We had plenty of opportunities to add to the three goals and it is a great boost for us beating a team as good as Man City 3-0 and deservedly as well.

"I don't think it is easy to keep City and I think you should pay credit to them for the way they kept them quiet."

Carroll himself was delighted to get off the mark.

"It's been a great day for us, getting my first goal and a great result all round," he said. "The reception I've got from the fans has been great, it's been fantastic since I got here."

Of his first goal he said: "It dropped nicely for me on the edge of the area and I hit it sweeter than I thought. We when out to put pressure on them and that's what we did and got goals early."