Tottenham's hopes of qualifying for the Champions League are getting thinner by the day.

By falling 2-0 at Chelsea on Thursday, Tottenham slumped to a second loss to a London rival in the space of four days in the Premier League -- after a 3-2 home defeat to Arsenal in the north London derby on Sunday.

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In between those losses came confirmation that England will have just four places in next season's expanded Champions League, and not five, with Italy and Germany already securing the extra places in next season's expanded competition.

That's another blow to Spurs, who are fifth and stayed seven points behind fourth-place Aston Villa with one game in hand. They still have to play Liverpool and Manchester City in their remaining four games so it is looking increasingly unlikely they will close the gap to Villa.

Headed goals by Trevoh Chalobah in the 24th and Nicolas Jackson in the 72nd were enough for Chelsea, who could yet salvage a place in one of the second- or third-tier European competitions from what has been an underwhelming Premier League campaign for a squad assembled at a cost of more than $1 billion.

Chelsea climbed above West Ham and into eighth place, two points behind Newcastle and three behind Manchester United in sixth. It's likely that two of those three teams will be playing in either the Europa League or Europa Conference League next season.

Tottenham have now won just one of their past 34 away league games against Chelsea, making it one of the most one-sided top-flight fixtures. The sole victory came in 2018, when Mauricio Pochettino -- the current Chelsea manager -- was in charge of Spurs.

"We are in a good place," Pochettino told the BBC. "We have amazing professionals working on set pieces. The team really showed in the way we wanted to build this way to play."

He described the first half as fantastic. "Then you have to contain and suffer."

Chalobah got on the end of a free kick by Conor Gallagher to loop a header over Tottenham goalkeeper Guglielmo Vicario and into the net to give Chelsea the lead. It was another goal conceded from a set piece by Spurs and that is becoming a recurring issue under manager Ange Postecoglou.

Jackson, who had a shot partially saved by Vicario and subsequently cleared off the line by Micky van de Ven in the first half, eventually got his goal when he was quickest to react after Cole Palmer's free kick rebounded out off the crossbar. Jackson did well to head the ball over two Tottenham defenders who were retreating toward their own goal line.

Tottenham's Australian coach Ange Postecoglou looked furious in the dugout throughout the first 45 minutes and his side came out of the second half with greater verve and determination but to no avail.

"I feel like we've lost a bit of belief and conviction in our football and that is on me to change that," he told Sky Sports. "We were nowhere near good enough. That is on me."

Tottenham are six points clear of Man United and might have to settle for a fifth-place finish, which would earn a spot in next season's Europa League.