The 25-year-old, who started in his side's 2-0 defeat to Nigeria during the group stage, said that representing his country in Russia is a moment he will never forget.
"I was just shaking with excitement," The Reading Chronicle quotes Bodvarsson as saying. "I called my family and let them know. They were so proud and happy. It was so exciting. I almost had a hard time sleeping the day before.
"Being on the pitch on that stage was such an amazing experience and it's something I will keep reminding myself about forever. It was the first time in the nation's history. We could feel the country behind us no matter what.
"Even though I didn't play in the first game, even getting a draw against Argentina was a huge win for Iceland as a country."
Iceland bowed out of the competition after losing 2-1 to Croatia in their final group fixture.