Mauricio Pochettino's men suffered their third straight defeat across all competitions at the San Siro on Tuesday night.
Christian Eriksen had opened the scoring for visitors early in the second half but Mauro Icardi and Matias Vecino's 85th and 92nd minutes strikes condemned Spurs to a defeat.
"We controlled the game in the first half and second half, played good, but I conceded the goal," Aurier was quoted as saying by Football London.
"It's difficult because I tried to play good today. The team, everyone played good today but I don't know. We conceded two goals. [We've got to] stay together for next week.
"It's a situation to stay focused. I'm sad for my team because today every player wanted to win the game and I play for a good team. I stay focused on the new challenge for next week."
"Every time, every moment you want to stay focused. Look, my team played good but that is a Champions League game."
For their next Champions League fixture, Spurs host Barcelona on October 3.