A 3-1 victory over Swansea on Saturday gave Conte's side a commanding lead as they head into the final third of the season, with the pressure resting firmly on the chasing pack.
The Premier League trophy will be heading back to Stamford Bridge if the Blues avoid any major slips during the final weeks and the Chelsea boss is convinced his players have shown they can hold their nerve after lifting the trophy during Jose Mourinho's reign.
"It's not easy to keep the concentration for the whole championship. But I have a lot of players who played and won in the past," said Conte. "They know very well the way that we must continue to try to keep at the top of the table, to try and win the title. For this reason, I'm lucky. I'm lucky to have a lot of players who, in the past, won a lot.”
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However, the Italian knows that he needs to do his part to keep the players on their toes. "If, sometimes, I can see some of them relaxing, it's right for me to try and help them be focused for every moment,” he said. "But honestly, it wasn't necessary for me to keep the concentration and focus of the players."
Chelsea appeared in danger of dropping points when Fernando Llorente cancelled out Cesc Fabregas's 19th minute opening goal, but Pedro and Diego Costa scored in the final 18 minutes to secure the win.
Conte was pleased with the way his side stuck to their task. "I have a team that until now has deserved to stay at the top of the table,” he said. "We are playing good football, with good intensity, scoring a lot of goals. Trust me, I'm very happy above all for my players. They are deserving of this. Every day I see them during the training sessions, the commitment and behaviour."
Fabregas was recalled to the line-up in place of Nemanja Matic and marked his 300th Premier League appearance with a well-taken strike before hitting the woodwork after the break.
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And in Conte's eyes, the Spaniard's contribution confirmed the options he has available in central midfield.
"Cesc played a really good game, but it's important for me to have these solutions and also to analyse the games, to understand when we need to have a player with more quality on the ball, and to lose something in height," he said.
The former Arsenal and Barcelona midfielder hasn’t seen much time out in the middle, finding it hard to displace midfield duo of Matic and N’Golo Kante but Conte praised the World Cup winner. "For me I consider Nemanja a top player, and also Kante, but also Fabregas. He's a really good player,” he said. "I'm really pleased to see him in this form despite not starting the last game in the league. This is the right way to continue."
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Swansea manager Paul Clement was convinced his side should have had a second-half penalty when Cesar Azpilicueta handled the ball, but he insisted the defeat will not affect his side's prospects of staying up.
"You never want to lose a game, but the performance doesn't damage our confidence. We've had some really difficult away games and picked up some good home results," he said.
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