Arsene Wenger admitted Arsenal’s hopes of a top-four finish hang by a thread after their 1-0 north London derby defeat to Tottenham at Wembley.

Harry Kane’s second-half header doomed Arsenal to an eighth league defeat of the season, seven of which have come on their travels, and left them marooned in sixth.

Fourth-placed Liverpool are six points clear with a game in hand and the gap could have expanded into double figures by the time Arsenal play their next league match, at home to Manchester City on March 1.

“It was a game we couldn’t afford to lose,” Wenger admitted. “It makes it much more difficult now, but we have to fight until as long as we have a mathematical chance.

In Pictures | Tottenham vs Arsenal north London derby | 10/02/2018 64 show all In Pictures | Tottenham vs Arsenal north London derby | 10/02/2018 1/64 Shaun Brooks/Action Plus 2/64 REUTERS 3/64 AFP/Getty Images 4/64 AFP/Getty Images 5/64 AP 6/64 REUTERS 7/64 REUTERS 8/64 REUTERS 9/64 AP 10/64 Action Images via Reuters 11/64 Action Images via Reuters 12/64 AP 13/64 AP 14/64 AP 15/64 AFP/Getty Images 16/64 AP 17/64 REUTERS 18/64 REUTERS 19/64 AP 20/64 AP 21/64 PA 22/64 AP 23/64 Action Images via Reuters 24/64 REUTERS 25/64 Action Images via Reuters 26/64 REUTERS 27/64 AP 28/64 AP 29/64 Action Images via Reuters 30/64 Getty Images 31/64 Getty Images 32/64 Tottenham Hotspur FC via Getty Images 33/64 Tottenham Hotspur FC via Getty Images 34/64 Tottenham Hotspur FC via Getty Images 35/64 Getty Images 36/64 Arsenal FC via Getty Images 37/64 Arsenal FC via Getty Images 38/64 Arsenal FC via Getty Images 39/64 Arsenal FC via Getty Images 40/64 Tottenham Hotspur FC via Getty Images 41/64 Getty Images 42/64 Arsenal training Arsenal FC via Getty Images 43/64 Arsenal training Arsenal FC via Getty Images 44/64 Arsenal training Arsenal FC via Getty Images 45/64 Arsenal training Arsenal FC via Getty Images 46/64 Arsenal training Arsenal FC via Getty Images 47/64 Arsenal training Arsenal FC via Getty Images 48/64 Arsenal training Arsenal FC via Getty Images 49/64 Arsenal training Arsenal FC via Getty Images 50/64 Arsenal training Arsenal FC via Getty Images 51/64 Arsenal training Arsenal FC via Getty Images 52/64 Arsenal training Arsenal FC via Getty Images 53/64 Arsenal training Arsenal FC via Getty Images 54/64 Arsenal training Arsenal FC via Getty Images 55/64 Tottenham training Tottenham Hotspur FC via Getty I 56/64 Tottenham training Tottenham Hotspur FC via Getty I 57/64 Tottenham training Tottenham Hotspur FC via Getty I 58/64 Tottenham training Tottenham Hotspur FC via Getty I 59/64 Tottenham training Tottenham Hotspur FC via Getty I 60/64 Tottenham training Tottenham Hotspur FC via Getty I 61/64 Tottenham training Tottenham Hotspur FC via Getty I 62/64 Tottenham training Tottenham Hotspur FC via Getty I 63/64 Tottenham training Tottenham Hotspur FC via Getty I 64/64 Tottenham training Tottenham Hotspur FC via Getty I 1/64 Shaun Brooks/Action Plus 2/64 REUTERS 3/64 AFP/Getty Images 4/64 AFP/Getty Images 5/64 AP 6/64 REUTERS 7/64 REUTERS 8/64 REUTERS 9/64 AP 10/64 Action Images via Reuters 11/64 Action Images via Reuters 12/64 AP 13/64 AP 14/64 AP 15/64 AFP/Getty Images 16/64 AP 17/64 REUTERS 18/64 REUTERS 19/64 AP 20/64 AP 21/64 PA 22/64 AP 23/64 Action Images via Reuters 24/64 REUTERS 25/64 Action Images via Reuters 26/64 REUTERS 27/64 AP 28/64 AP 29/64 Action Images via Reuters 30/64 Getty Images 31/64 Getty Images 32/64 Tottenham Hotspur FC via Getty Images 33/64 Tottenham Hotspur FC via Getty Images 34/64 Tottenham Hotspur FC via Getty Images 35/64 Getty Images 36/64 Arsenal FC via Getty Images 37/64 Arsenal FC via Getty Images 38/64 Arsenal FC via Getty Images 39/64 Arsenal FC via Getty Images 40/64 Tottenham Hotspur FC via Getty Images 41/64 Getty Images 42/64 Arsenal training Arsenal FC via Getty Images 43/64 Arsenal training Arsenal FC via Getty Images 44/64 Arsenal training Arsenal FC via Getty Images 45/64 Arsenal training Arsenal FC via Getty Images 46/64 Arsenal training Arsenal FC via Getty Images 47/64 Arsenal training Arsenal FC via Getty Images 48/64 Arsenal training Arsenal FC via Getty Images 49/64 Arsenal training Arsenal FC via Getty Images 50/64 Arsenal training Arsenal FC via Getty Images 51/64 Arsenal training Arsenal FC via Getty Images 52/64 Arsenal training Arsenal FC via Getty Images 53/64 Arsenal training Arsenal FC via Getty Images 54/64 Arsenal training Arsenal FC via Getty Images 55/64 Tottenham training Tottenham Hotspur FC via Getty I 56/64 Tottenham training Tottenham Hotspur FC via Getty I 57/64 Tottenham training Tottenham Hotspur FC via Getty I 58/64 Tottenham training Tottenham Hotspur FC via Getty I 59/64 Tottenham training Tottenham Hotspur FC via Getty I 60/64 Tottenham training Tottenham Hotspur FC via Getty I 61/64 Tottenham training Tottenham Hotspur FC via Getty I 62/64 Tottenham training Tottenham Hotspur FC via Getty I 63/64 Tottenham training Tottenham Hotspur FC via Getty I 64/64 Tottenham training Tottenham Hotspur FC via Getty I

“There was more at stake than just the derby, I said that before the game, that’s why it’s so disappointing to lose the way we lost it.”

Even if Arsenal fail to overhaul Liverpool and Chelsea to finish in the top four, hope is not over in their bid to ensure their Champions League absence is a brief one.

Winning the Europa League would earn them a seat at Europe’s top table once more but, as holders Manchester United proved last season, balancing the Premier League with continental matters is far from simple.

Wenger has previously expressed his reticence at jettisoning the Premier League to focus on Europe and reaffirmed that it would be some time before Arsenal’s priorities change.

“It’s too early,” he said. “Football is not about switching off for three games and switch it on for one.

“Manchester United decided that once they were in the semi-final, we are far from the semi-final. I think we have to fight to have a chance to come back.

“For me it’s a very disappointing result. The priority has to be to be in the Champions League through the Premier League. I’m not a great fan of qualifying for the Europa League through the Champions League.

“If it’s an opportunity we have to try and take it as well, but the priority is still the Premier League.”

Arsenal Europa League odyssey begins again next Thursday, when they travel to Swedish side Ostersunds for the first leg of their round-of-32 tie.