Giroud scored with a brilliant overhead kick in the 85th minute to see Arsene Wenger's men to a 1-0 victory in Belgrade.
The France international said he would have preferred to link up with a team-mate, but he had no options before he superbly put his effort into the top corner.
"In that position, I can control the ball and try to play with another team-mate," Giroud told UEFA.
"But I didn't see anyone so I tried to take it as I can, a little bit like [against Crystal] Palace [in January], I've been a bit lucky because it's top corner and it's (in) the back of the net.
"It's nice for the team, I'm happy for the team because we've been resilient until the end and we keep believing in our game, and we knew it was going to be a tough game and just needed to be patient and play our game with our qualities.
"It has been very difficult because it's an amazing atmosphere here, special atmosphere, the crowd is behind their team and it was a tough game but we're very pleased with the three points."
The win was Arsenal's third from as many games in Group H and came after Red Star had been reduced to 10 men through Milan Rodic's red card.