Spurs were lacklustre in a 1-0 Group C win over already-eliminated Partizan on Thursday - Stambouli scoring the game's only goal in the 49th minute.
The French midfielder's strike was his first for the club since joining from Montpellier on transfer deadline day.
And he dedicated his goal to those in the military, after admitting there was significant room for improvement for Mauricio Pochettino's side.
"It was very good to score and win," Stambouli told ITV4.
"It is only positive things for us. We play good teams who love to fight and we need to improve.
"My celebration [a salute after scoring] was for all military round the world. They fight for peace."
Tottenham were sluggish in the first half but did improve after the break, only to miss a series of chances.
Youngster Harry Winks got a chance to make his debut late in the piece though, and he dubbed it a life highlight.
The 18-year-old is quoted as saying on Tottenham's official Twitter account: "It's the best moment of my life. It's a dream come true. I loved every minute of it."
Besiktas' 2-2 draw at Asteras Tripolis sees Spurs top Group C by two points heading into matchday six.
That means that avoiding defeat in Turkey next month will be enough for Spurs to finish first in the pool.
