The 22-year old striker netted twice in the 2-1 win over Luxembourg and almost had a third but was flagged for offside.
It would have been the first treble for the Scots since Colin Stein netted four against Cyprus in a World Cup qualifier 43 years ago and although Rhodes was unaware of the record, he was more than happy to contribute to a victory.
"I didn't realise how long it was since a Scotland player last scored a hat-trick. That's a shame I didn't manage to equal it," he said.
"But it would be selfish of me to want a hat-trick. The main thing is winning the game, not scoring goals.
"It's just pleasing that we got the win and a couple of goals is more than I could have asked for in an international game.
"I thought I had the hat-trick when Liam Kelly chipped one over, but it wasn't to be. It's one of those you sometimes get, and sometimes don't.
"I didn't know what was going on behind me, so I couldn't really say for sure. The lads were asking me at the end. Some of them thought I might have been in line and others thought I was half a yard off.
"I suppose it was one of those touch-and-go ones. But I couldn't really see."