Ramsey offered Bellamy the chance to take a late penalty kick but the forward declined, with the Arsenal playmaker eventually stepping up only to have his effort saved.
Following a hard-fought victory Ramsey has declared that the win will prove an important confidence boost for his young side, while insisting the three points were earned for Bellamy.
He told Sky Sports News: "It was important tonight, to start strong and we managed to do that.
"We're delighted in there. Obviously it was Craig Bellamy's last game at home and we wet off with a win for him. He's had a fantastic career so that win was for him tonight.
"I offered him the penalty and he said no you're the captain of this team you take it. All credit to him but I was I had given it to him now."
Coleman's side will now look to ensure they stay ahead of Scotland in Group A, with their final qualifier coming away to in-form Belgium on Tuesday night.