England strolled to a 5-1 win in the match in Podgorica, with Henderson coming off the bench in the second half and grabbing a late assist for Raheem Sterling's goal.
The game was marred by racist chants from fans aimed at England players, with UEFA having now opened an investigation into the matter.
Henderson picked up a booking in addition to his assist, as tempers flared and the chants from the crowd continued.
But Savic has highlighted a different incident, saying the Liverpool midfielder was disrespectful toward one of his team-mates when sarcastically offering to trade jerseys after the game.
"We all know they are a much bigger team than us but sometimes I feel very bad to be playing the same sport as some players," the Atletico Madrid defender said.
“Jordan Henderson, for example, sarcastically told our player after one normal clash he would give him a jersey after the match.
“It is ugly and disrespectful. I told him he was good enough not to act like that.
“We are proud and I’d rather play with this team and concede five goals and not with some arrogant players from England.”
England now top Group A of Euro 2020 qualifying after starting their campaign with wins over the Czech Republic and Montenegro by a combined score of 10-1.