Ole Gunnar Solskjær believes Manchester United are heading back towards the top after his team recorded a third victory over Manchester City this season at an Old Trafford which celebrated vociferously.

Goals from Anthony Martial and Scott McTominay – both due to mistakes by City’s keeper, Ederson – ensured United recorded a league double for the first time since the 2009-10 campaign. This was also an eighth clean sheet in 10 outings.

Solskjær said: “The desire, attitude, commitment, connection between fans and players pleased me most. With all the clean sheets we have been getting it’s impressive, we are getting better. At times we pressed them, pushed them back. We tried to be aggressive. We made them make mistakes and we are happy with the result.

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“For me it shows we are on the right track and improving and we are Manchester United and looking to catch the teams in front of us. [But] this is one game.”

Martial’s goal made him the first United player to score home and away in the league against City since Cristiano Ronaldo 13 years ago. The centre-forward’s 30th-minute volley came from a Bruno Fernandes free-kick, Ederson allowing the ball to squirm in.

Solskjær said: “Anthony and Bruno have hit if off. It is a privilege to be a manager of a squad with this attitude. You can’t ask for more. They are going to improve as players as well. Those little things will come but it is a privilege and they want to listen to advice. For our players to beat a team like Manchester City is fantastic, I am delighted for them.”

Victory in the 182nd derby takes United to 45 points, three behind Chelsea, who are in fourth place in the Premier League. “It’s a derby, the fans love it, the players love it,” Solskjær said.

“For our players to beat the team that’s Man City, with the [injury] problems that we’ve had, it’s fantastic. We played against an absolute top, top team.”

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McTominay’s finish came from around 40 yards out, six minutes into added time after Ederson threw the ball to the midfielder. He said: “That was such a sweet moment, especially in a game where we could have done with another goal earlier on to finish the game.

“Credit to the boys who were top drawer. We had a sticky first 15-20 minutes but you see how much it means to the boys in a derby again.

“We have to keep going. It’s a game [from which] we have to take confidence but we have to get some proper results over the next few weeks to keep this run going.”

Of his finish the Scot said: “I read the goalkeeper. You give yourself half a chance because they’re rushing. You get there before [Benjamin] Mendy and it’s such a beautiful feeling in front of our fans in the last minute.

“Can’t get too carried away but we’ve got to keep going and keep pushing for the Champions League.

“Every game is special but these games against Liverpool, Arsenal – they’re very special atmospheres. These fans, through thick and thin, they’re there every week. Just to hear two or three people singing your name, never mind the whole Stretford End, is beautiful.

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“I know one or two City fans, so it will be good to rub that in their faces as well.”

Pep Guardiola refused to criticise Ederson. “He is an extraordinary player in the buildup, the saves – sometimes it happens,” the City manager said.

He did, though, contradict Bernardo Silva’s characterisation of the performance as unacceptable. “I do not agree with him,” he said. “We played good. We missed a little in the final third but the second half was better and it was a good performance. We play the same way, tried the press and defended well and we did well.”