Mathieu Flamini opened the scoring for the visitors in the first half, with Nacer Chadli's cross being turned into his own net by Calum Chambers to level matters up soon after the break.
Flamini's opportunistic strike settled the tie, though, as we bowed out of the competition despite a brave showing.
Spurs (4-2-3-1): Vorm, Trippier, Fazio, Wimmer, Rose, Dier (Njie 85), Carroll, Townsend (Son 67), Eriksen, Chadli (Alli 75), Kane. Substitutes (not used): Lloris, Walker, Vertonghen, Winks.
Arsenal (4-2-3-1): Ospina, Debuchy, Mertesacker, Chambers, Gibbs, Arteta, Flamini, Campbell (Sanchez 67), Ramsey, Oxlade-Chamberlain (Walcott 89), Giroud. Substitutes (not used): Macey, Monreal, Bellerin, Ozil, Iwobi.
Goals: Spurs – Chambers (own goal) 57; Arsenal – Flamini 26, 78.
Yellow cards: Spurs – Alli; Arsenal – Arteta, Flamini, Debuchy.
Referee: Andre Marriner.