José Mourinho said that Manchester United's hopes of defending their title were effectively over after Chelsea beat the champions 3-1 at Stamford Bridge to leave them 14 points behind the leaders Arsenal.

David Moyes, the United manager, vowed to fight on and insisted there was little between the teams, apart from a couple of defensive set-piece aberrations that allowed Samuel Eto'o to score his second and third goals.

As the dust settled on Mourinho's 100th Premier League win, the table looked bleak for United. They are 13 points behind second-placed Manchester City and 12 off Chelsea in third. "Maybe if I say [United are out of title contention], some people from United would ask: 'Who am I to say that?'" Mourinho said. "But I don't think David will be upset if I say the reality: 14 points difference and 13 and 12 [to the others]. Can they recover to one of those teams? They can but to three of them? It needs three teams to have almost a collapse. What I hope they do is to beat all of them to finish top four."

Moyes has not beaten Mourinho in 10 attempts and this defeat, United's seventh league defeat of the season, was marred by the injury-time dismissal of the captain Nemanja Vidic for a lunge at Eden Hazard. He will be banned for three matches. The United full-back Rafael da Silva was lucky to escape a red card later on in injury-time for a studs-up, two-footed tackle on Gary Cahill.

"I thought Vidic wasn't a sending off but I've seen Rafa's and I think that could have been one," Moyes said. "There were two tackles. People want their players to tackle. I thought one was a yellow card. On another day, the other was a red."

Moyes did not dwell on the 38th-minute incident when the Chelsea defender César Azpilicueta appeared to catch Danny Welbeck before the striker shot inside the area. "It would have been a soft penalty," Moyes said and he dismissed questions about a United crisis. "Crisis is your word, not my word," he said.

"What we won't do is throw the towel in until we can't get there [to the title]. The job is to try to finish first. There are no clever answers: it's the next game. We'd lost one in six before today in the league and I didn't think there was a big difference between the teams today. The difference was our defending to set-pieces.

"Confidence is fine. It's a difficult task but it's perseverance … doing what is right. We have players to come back and this is a project that I'm going to improve as we go along. It's a massive challenge. I'd hoped I'd be in a far better position than this but we're not. As a football person, it's a great challenge to have. Of course, I was hoping to win more and compete a bit more but that'll come."

United started and finished brightly – they had a few chances to score before the substitute Javier Hernández did so on 78 minutes – and Moyes argued they were merely undermined by Eto'o's deflected opener and then the set-piece lapses.

"I thought we played quite well throughout but it came down to two set-pieces and we didn't defend them well," Moyes said. "That was probably the difference. You always practice. It's hard to do more. We had as many opportunities as Chelsea and didn't take them. We had a big part of the game but we didn't score when we had chances and we didn't defend set plays well enough.

Mourinho lost the substitute Fernando Torres to lateral knee ligament damage, which will rule him out for "weeks" but this was Eto'o's day. "It was a fantastic moment for someone to score a hat-trick and against Manchester United," Mourinho said. "It was a pity for Nando but now it's time for Demba Ba. He's had a fantastic week, working well. Now go. It's his chance."