Eight points adrift of Spurs with only seven games remaining, the Blues' prospects of closing that gap are slim.
Antonio Conte's future was already in serious doubt before kick off. Little wonder, then, that he entered the media room as sullen as he has ever looked in west London, as he navigated a painful press conference inflicted on him by Dele Alli's brilliance.
The Chelsea head coach was a hero last season after leading the club to the title. Transfer market frustration last summer, though, proved merely a precursor to a limp title defence.
He may have distanced himself from the decision-making process, but the club hierarchy are not in turn happy with the Italian's strategy to point fingers at others.
After Sunday's match, the former Juventus boss said that he has been getting the most out of his players this season, insinuating that they are no longer good enough to battle for a finish above Spurs in the table.
"I'm sure about this because I think... we are working," he said. "We are working very well, very hard, and the commitment of the players is top. Despite this, you stay in this position. We must be a bit worried about this.”
Meanwhile, Conte's friend Gianluca Vialli has said that the Blues head coach "can't wait to leave Chelsea".
Even FA Cup success would fail to paper over the cracks of what has been a thoroughly demoralising season. While Manchester City and United are operating in a different financial market to the Blues, Liverpool and Tottenham have taken advantage of their long-term stability.
The Italian signed a new contract in the summer, but he merely accepted a pay-rise without extending the length of his deal which expires in 2019. In contrast, Spurs boss Mauricio Pochettino and Liverpool counterpart Jurgen Klopp operate seamlessly within their club's system, Conte has brought more tension to an already chaotic club.
The friction between the 48-year-old and Chelsea's hierarchy began after he sent a text message to Diego Costa to say he was no longer needed. Costa knew he was exiting the club, having pushed to do so in the two transfer windows prior, but he reacted angrily while away with Spain on international duty.
Moreover, the coach got frustrated by the club's refusal to sign a host of older players as they looked for value in the transfer market in the shape of youngsters. When the Blues did target their manager's prefered options - Juventus's Alex Sandro, Napoli's Kalidou Koulibaly and Roma's Radja Nainggolan, for example - they missed out.
Of the eight players they did sign, only Antonio Rudiger was consistently of the standard expected. Five, meanwhile, arrived either injured or having just overcome injury.
Chelsea spent big money, but in terms of net spend, they sit a long way behind Manchester City. Conte wanted Alexis Sanchez from Arsenal, but the board could not compete for his signature as Manchester United offered him a huge wage package.
This inability to sign players of the required standard had a directly negative effect on the team, most notably against Burnley, when the manager was left woefully short of options. Similarly, in a fixture against Bournemouth, he was forced to use Eden Hazard as a false 9.
Closing the gap off-the-pitch is a job for Marina Granovskaia and the club's office-based staff, but they need to learn from the appointment of Conte and hire the right manager, rather than the best manager next time.
Paris Saint-Germain and the Italian national team are the main options for Conte after Chelsea, but in the meantime, the Blues should look to someone who can work with smaller budgets.
Additionally, someone is required who can integrate the incredible talent from the youth academy, while also making the most out of the club's loan system. Chelsea need to be patient with that person and not dangle a sword over their heads to win trophies.
Ironically, they need someone like Pochettino, who is committed to improving the club's playing staff gradually, despite the limitations that he has faced with Tottenham.
It could be a long road to recovery for Chelsea. The Europa League is exactly where they deserve to be.