A defiant David Moyes said he would correct Manchester United's faltering start to life without Sir Alex Ferguson after his side responded to their derby mauling with a 1-0 victory over Liverpool in the Capital One Cup.

The United manager admitted to relief after Javier Hernández's 46th-minute goal secured the Premier League champions a fourth-round tie at home to Norwich City. It not only gave Moyes some breathing space following the 4-1 defeat by Manchester City at the Etihad, but also ensured he has made the best start to a managerial career at Old Trafford since Sir Matt Busby. "Everyone seems to be picking a stat out about me at the moment but that is a good one," he said. "I have not had that many."

Moyes then insisted he had not been hurt by the criticism of his brief United tenure, with league defeats at City and Liverpool sandwiching a low-key end to the transfer window. He said: "It is not frustrating because I will sort it. I will fix it. I will turn it around. I have got no doubt about that. What have I learned? We know we have to improve. I am still getting to know the players. They are a really good team, they won the Premier League last year, but we need to make sure we improve."

United fielded a much-changed team for the third round tie, in contrast to the strongest Liverpool side that Brendan Rodgers had available, despite the pressure on Moyes following Sunday's derby defeat. The United manager said: "There was certainly some relief as it was a big day for us. We lost at Anfield a few weeks ago, we lost at the Etihad last week, so we wanted to put that right. I thought it was a really good game, an exciting game of football from both teams.

"In truth, I didn't think there was much in it. If you look at the two games, they have both been won by a set piece. We made a lot of changes to make sure we made full use of the squad, to get them some playing time. Liverpool have started the season well. It was not a risk, with the players we have at Manchester United. They are all internationals and first-team players. There are no reserves in this squad. Everyone one of them could play in the first team. Some of the performances were excellent."

Moyes added: "What was important was that the whole club showed we were hurt by the game on Sunday. We did not perform to our levels. But they have gone out and the players have done a great job to get us a big result. I am really pleased with them."

The tie was dominated by Luis Suárez's return for Liverpool after a 10-match suspension, with the Uruguay international hitting the bar in a lively 90-minute display. "The result is not good because we lost but the feeling is good because we played very well, we created chances but we missed," Suárez said.

"I know it was a difficult moment but for myself and for the team it's very important I'm back because I can help the team, and being off the pitch I can't. We'll keep going for the week and for the next game. All the time I try my best on the pitch. I'm here to help the team and help Liverpool and I'll try my best."