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The midfielder transferred from Partizan to Ibrox in the summer, in a deal reportedly valued at around £4.6 million.
Leaving a club where he was captain and a regular fixture, Dragojevic has only made two appearances in the Scottish Premiership for Rangers, including a three-minute cameo against St Mirren.
The club also bolstered their midfield with the summer signings of Dan Neil and Cammy Devlin, adding to a position already occupied by Nico Raskin and Tochi Chukwuani.
Despite the competition and lack of game time, Dragojevic has no regrets about signing for Rangers.
The Serbia international said: "It was the right move. Rangers is a club with a championship mentality, always looking to win.
"The fans have welcomed me and I’m glad they recognised my desire and energy, which is similar to the energy of the club."
He added: "I couldn’t believe how many messages of support I received telling me to bide my time, that it would come, to be patient.
"It was fascinating to me how much a fan wanted to help a player continue to believe in himself.
"They love the club and the football so much and really push Rangers forward."
The 20-year-old believes he is well suited to the Scottish game, and revealed that the pace and intensity of football in Scotland was a factor in his decision to move.
He said: "There are many quality teams and players in Serbia, but the Scottish league is faster and physically stronger.
"There is a lot of intensity and that was one reason why I chose it as my next step.
"In Partizan my position required a lot of running, dueling and intensity, so this is the right league for me."
Despite being a midfielder, Dragojevic doesn't mind playing in different positions if needed.
He said: "I’ve always put the team before myself, that’s how I was taught from a young age.
"I really don’t have a problem playing in whatever position is needed for my club or the national team."
Dragojevic also appreciates Glasgow and Scotland's deep-rooted tradition and how this is reflected in Rangers.
He said: "Glasgow is a very beautiful city, and everywhere in Scotland you can feel how much they care about tradition.
"It’s the same at Rangers. From day one they made sure I felt like I had been there for a long time, that I learned things about the club and how proud they are of their history."