Ukrainian referee Yevhen Aranovskiy took the players off the field after 38 minutes of the Group C game with the teams drawing 0-0. The players returned to the White Hart Lane pitch about 10 minutes later and Spurs won the match 1-0.
Police arrested the three pitch invaders who appeared to be wearing identical branded t-shirts and British media reported that it could have been part of a marketing stunt.
"It was strange. You can expect that kind of thing to happen anywhere in the world but not in England and for it to happen three times in one half was odd," said Partizan coach Marko Nikolic.
"I think it was a bit disturbing for both sides but I was not worried about my players' safety. I think the referee made the right decision to take the players off. It sent the message that it must not happen again."
Tottenham said in a statement: "Three pitch invaders at tonight's match have been arrested and are assisting police with their enquiries,"
"We shall provide an update as soon as we have established the full facts. We apologise to fans for the disruptions caused by this totally unacceptable behaviour."
Spurs manager Mauricio Pochettino told reporters: "(For) all the people that love the game it was very disappointing, a very strange situation."
