They nearly had the ideal start when Marcos Alonso's half-volley was tipped onto the bar by Brad Guzan with the game just 90 seconds old.
Chelsea manager Antonio Conte during the press conference.
"We have to reflect on what has gone wrong, learn and produce better".
Despite his side's total control of the game, the ever feverish Conte prowled the touchline as usual, gesticulating wildly and yelling commands to his players.
Former Chelsea midfielder Gus Poyet believes Chelsea deserve to win the title because they've been the most consistent team. In fact it's the lowest point of my life, not just my career.
Meanwhile, Middlesbrough would be dropped back to the Championship after their single season's stay in the top flight.
Elsewhere, Jurgen Klopp's Liverpool remain third despite only managing a draw at home to Southampton, and they are now just a point clear of Manchester City after they dispatched Sam Allardyce's Crystal Palace 5-0 at the Etihad Stadium on Saturday.
"I'm frustrated and disappointed". "Obviously we've come up short".
He said: "In this case it is important to celebrate your win because for us it means we are very close to winning the title. We haven't scored enough goals".
"They might not have the pressure to win the game in terms of their league position but nobody wants to be the team that loses and let other guys have their parties".
Babayaro, who also enjoyed spells with Newcastle United and Anderlecht, went on to praise Conte for the wondrous job he has done during his first season at Chelsea.
"It's not about my situation, it's about how we reflect over the summer". It's great. Now we need to do another step.
In the match played last night against Middlesbrough, Chelsea's player was on a mission.
"The most important thing is we finish the season strong, we make sure we gain more points and everything moving forward will be towards getting members of the football club back to the Premier League as soon as possible".
"Conte has done a great job in his first season", said Babayaro, who was speaking on the Alan Brazil Sports Breakfast show.
The reason for wanting to deny Fabregas his assist was because, as can be seen in the footage above, the ball hit Boro's Fabio as it went to Costa.
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