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Antonio Conte admitted Chelsea’s shortcomings in front of goal were highlighted again in the 1-0 win at Swansea.
The Blues missed a number of chances and had to endure a difficult second half as the home side threatened an equaliser.
The points kept alive their hopes of pipping Tottenham to a Champions League place. It moved them to within two points of the north London side, who are at home to Watford on Monday.
But Chelsea boss Conte said: “Our top scorer (Eden Hazard) has scored only 12 goals.
“If your best scorer scores only 12 goals it is very difficult to fight for something important in a season. This is the reality. The stats speak very well.”
Spurs slipping up could pave the way for Chelsea to snatch fourth place, but Conte is realistic about his team’s chances.
“The only way to put pressure to Tottenham is to get three points in every game, but the situation is not in our hands,” Conte said.
“We got three points and it was very important for us if we wanted to keep hopes alive and achieve Champions League football.
“It was a tough game, but we knew this against a team who is fighting to avoid relegation.
“In the last five games at home, they won four and drew one. They played a good game, especially in the second half when they tried to push us.”