• Chelsea manager calls for players to focus on winning six games to secure title • ‘Only if you win the title do you write the season down in history’

Antonio Conte has told his players to assume Tottenham Hotspur will win all of their remaining Premier League games and, having killed off Manchester City’s faint hopes of mounting a late challenge, urged Chelsea to concentrate on securing the six wins they need to reclaim the title.

The Italian became the first coach to do the double over a Pep Guardiola team after Eden Hazard’s first-half brace, and a strong defensive second-half showing, secured a narrow victory over City. The success maintained the leaders’ seven-point advantage over Spurs – who scored three times in the last few minutes at Swansea to secure a sixth successive win – and pepped confidence after Saturday’s rare and untimely loss to Crystal Palace.

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“At this point of the season the pressure is very high, and to drop points would have given hope to your opponents,” said Conte. “So this is a good win for us against a top team, with great players and the best coach in the world. When you face this type of combination, it’s tough to win, especially after a defeat to Palace. So this was another step – a big step – against a great team with a lot of qualities.

“For all my players and me, only if you win [the title] do you write the season down in history. If we don’t do that, it will have been a good season, but not a ‘great’ season. So the only message I have given my team is that [to assume] Tottenham must win their last eight games. So we must make six wins and the 18 points we need. If we do this, we win the title.

“In Italy it’s easier for me to find the right words to motivate my players. I am studying English but I’m not at a great level to give great motivational talks. But I try. I push sometimes with words, sometimes with my hands. Numbers now … six wins. Six wins. There is a long way to go.”

Conte rejoiced in Hazard’s 12th and 13th goals of a productive season with Chelsea, who travel to Bournemouth on Saturday, unlikely to be sanctioned by the Football Association for Diego Costa’s ugly lunge, while grounded, on Vincent Kompany. The striker had caught the City centre-half on the knee 20 minutes from time, but the referee Mike Dean appeared to have witnessed the incident, thereby ruling out the possibility of retrospective action. “It’s very difficult to see this type of situation during the game,” offered Conte. Guardiola shrugged off mention of the challenge.

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The City manager conceded his side’s priorities have become Champions League qualification and the FA Cup, though he claimed to be hugely satisfied with his team’s performance even in defeat. “Today the Premier League has gone, so we have to think about finishing in the top four,” said Guardiola. “Absolutely, we were the better team, but they got six points against us over the two games and we got zero. Football is also about results.

“But the way we played? I’m so satisfied. I’m a lucky guy to be here with them. I was happier today with the way we played compared to Arsenal on Sunday, and we got a point less. I don’t want to see the way we played against Arsenal again. We were 1,000 miles better than in that game. Of course, I’d have liked to have taken one or three points, but, in the boxes, Chelsea are better than us. Hopefully next season we’ll be stronger to do that. We have to analyse things for next season because we have to win games like this. But, for now, congratulations to Chelsea.”