Antonio Conte criticised his players for allowing a lead to slip away against Manchester United and accepted Chelsea may struggle to finish in the top four.
Willian deservedly put the visitors ahead at Old Trafford and Chelsea dominated possession but Romelu Lukaku quickly equalised and substitute Jesse Lingard headed in the winner with 15 minutes remaining.
The result, coupled with Tottenham's victory over Crystal Palace, left Chelsea in fifth place in the Premier League table, while United climbed back above Liverpool into second.
Conte said: "For sure we must be disappointed for the final result. I think today we had a good chance to get three points against a competitor for a place in Champions League but at the end we are talking about another defeat and we must be disappointed because when you have this type of situation you have to manage the game better and you must be able with experience, with maturity, to get three points."
Asked what it would say about Chelsea if they do not qualify for the Champions League, Conte said: "I don't know but this could be a possibility for sure.
"I am repeating the same concept many times but in this league to find a place in Champions League is not simple. There is this risk to stay out of the Champions League. We must be ready to fight, to be concentrated and to understand that this target is an important target for us but it won't be easy."
Conte made a tactical decision to bring off playmaker Eden Hazard just before Lingard scored, saying afterwards he felt the Belgian had run out of energy. The Italian also again spoke up in favour of VAR after Alvaro Morata was shown to be onside when he found the net late on.
Opposite number Jose Mourinho praised his players for their attitude in turning around the game after Chelsea dominated the opening half an hour.
The United boss said: "You can only win against the top teams with that humble attitude. We can be speaking about tactics and positions and football science but to win against the top teams the attitude has to be really special and the players showed that.
"The beginning of the game was blue. We took a little bit of time to adapt to some new positions on the pitch, the way we were playing. We scored the winning goal that I think in the end we deserved."
Lukaku has had plenty of critics for his performances this season, and this was not a faultless display by any means, but the Belgian scored the first and created the second as well as forcing a fine save from Thibaut Courtois with an acrobatic volley.
"He played fantastically well," said Mourinho. "He had the same start as the team. He was a little bit lost. But then he went together with the team and probably the people go home with the image of that incredible sprint that could hand him a goal.
"We started the game with three points difference to Chelsea and we could finish with the same or with six points. It was important for us to open this gap a little bit."
There was as much attention on the touchline as the pitch given the history between Mourinho and Conte but the animosity between the two men was put aside as they shook hands before and after the match.
Mourinho said: "The handshake doesn't need any words. I think that is what me and Antonio want to show to everyone. Mourinho and Conte they are not two ordinary persons in football. We have a history, we have an image, and I'm really happy with that."
Conte added: "You wanted to see the shake hands and we did this. Now stop."