The Blues' chances of success hinge on Antonio Conte getting his team selection and tactics right for each of their remaining five matches, starting with Saturday's Premier League fixture away to Swansea City.
After a limp title defence, and likely failure to finish in the top four, Conte pinpointed Chelsea's inability to finish teams off as their number one problem this season.
"It's not so simple", Chelsea head coach Conte said.
I know that when you have to go to play this competition, the World Cup or European Championships, it's important to have players with great experience because the pressure will become very strong for everyone.
Asked if it was realistic for Chelsea to overhaul Spurs and clinch Champions League qualification, Conte puffed out his cheeks.
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The Blues reduced the gap between them and fourth placed Tottenham Hotspur who host Watford at the Wembley Stadium on Monday to two points.
"I think Cahill developed a lot this year, but we have three or four players who take responsibility, who try to lead the team".
But the French midfielder insists he will be fully fit when the World Cup kicks off this summer in Russian Federation.
Olivier Giroud was signed from London rivals Arsenal in January to bolster Conte's attacking options, but the Frenchman has so far managed to only net twice in the Premier League since switching allegiances. I repeat, it is very important for us to try and do our best until the end. He has great experience.
"I think then there are, for sure, other situations that we have to improve, but (against Swansea) I think we had good balance with the three midfielders".
"But, at the same time, I have always shown great respect for Southgate".