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It was a troubled night for Xabi Alonso's side, who lost at home in the league for the first time this season.
The Blues, who would have moved level on points with third-placed Brighton had they won, created the better chances when the game was goalless but visiting goalkeeper Antonin Kinsky saved well from Cole Palmer, Jordan Henderson and Pedro Neto.
Chelsea handed 21-year-old Mike Penders his opportunity in the absence of Martinez and he did well to keep out Omar Marmoush's side-footed effort from Andy Robertson's left-wing cross and also denied Tel.
But the Belgian was to blame for the crucial opener, and may feel he should have also done better with Tottenham's second goal.
Chelsea missed injured striker Joao Pedro, with Morgan Rogers ineffective in a false nine role, while 19-year winger Geovany Quenda also struggled to have an impact as he started a league game for the first time since a £40m summer move from Sporting.
Boss Alonso will also have to make do without Palmer for Wednesday's Carabao Cup last-16 tie at Anfield against Liverpool after the forward's first career red card.