Costa wrapped up the win with his first Premier League goals since March 6.
Tottenham Hotspur must learn to "get over the finish line", striker Harry Kane has said after the club failed to convert a dominant performance into a victory against Chelsea in the FA Cup semi-final.
The White Hart Lane-based outfit did edge closer to their rivals in the last Premier League outing, beating Bournemouth 4-0 before Antonio Conte's men suffered a disappointing 2-0 defeat against Manchester United at Old Trafford.
'But we must think this race is open.
The Blues are hoping to win a domestic double this term after having booked their place in the FA Cup final against Arsenal next month.
"It's probably the best spell I've had as a manager, in terms of an eight-game period, given who we've beaten and how we've done it".
"It's normal we have to push to try to keep this position until the end".
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The German giants were left furious after a string of controversial decisions saw them knocked out of the Champions League . Ronaldo scored a hat trick on the night to become the first player to score 100 goals in the Champions League .
Gary Cahill has worn the armband in Terry's absence this season and appears to be the leading candidate to succeed his fellow centre-back in 2017-18, but Hazard's name has also been mentioned due to his role as Belgium captain. "He's very important for us, his confidence is very important for us".
Blues head coach Conte said: "We passed a big step, a big psychological step after the defeat against United". They had no pressure so you can enjoy these type of games when you face the team who are top of the league.
Conte reckons players can only be great by playing as part of a team.
Southampton pulled one back at the death, but there was no time for them to fight again as Chelsea won the match 4-2.
Cahill felt his second goal came at a pivotal time, adding: "It was a great time to score the second goal because we went in at half-time with our tails up".
"It's a good win - I'm pleased with the fantastic effort". Sometimes he was lacking in different circumstances but I was always confident about him. "We must be compact and think our target is really [more] important than the other teams'". Our answer was very good.
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