"We won't be complaining to anyone. We're Stoke and we don't complain," Pulis told reporters after the match ended in a 3-1 win for the home side.
A cigarette lighter was thrown at Ricardo Fuller after he opened the scoring for the vistors at the Inonu Stadium while Jermaine Pennant was initially unable to take a corner because of the objects raining down on him during the second half.
Several Besiktas players appealed for calm from their fans and Polish referee Marcin Borski stopped play and spoke to the home bench before the situation calmed down.
Besiktas could still be in trouble with UEFA if the referee details the incidents in his match report.
Pennant said: "I was about to take a corner and I was getting pelted with everything: lighters, euro coins; I was thinking of picking one up and putting it in my sock.
"I didn't want to take it because every second I could see things flying past me. Until that stopped I didn't feel comfortable taking the corner and then obviously the referee called me away."
Stoke had already qualified for the last 32 before the match, but Besiktas made sure of their place with their victory and top place in Group E.
Fuller put Stoke ahead with an early goal but the turning point came after an hour when Stoke's central defender Matthew Upson conceded a penalty and was sent off for bringing down Hugo Almeida.
Manuel Fernandes made it 1-1 with the penalty before Mustafa Pektemek headed Besiktas ahead after 74 minutes and Edu scored with a brilliantly-struck curler eight minutes from the end.
Besiktas won the group with 12 points, followed by Stoke on 11. Dynamo Kiev and Maccabi Tel Aviv, who drew 3-3 in their match, were both eliminated.
