Davies will not be back until at least September after suffering the setback against Arsenal at the Emirates Stadium on Saturday.
But Davies is already channelling his thoughts on making a return to action as soon as possible with Martin O'Neill's side.
"It's going to be a shame to miss the run-in but that's football and you have to accept that.
"I knew straight away what it was. I'd just turned to get back into my position. I didn't do anything too strenuous and I felt and heard the Achilles pop.
"I've been told by someone who's done it before that you hear it. It's like a gunshot. Zat Knight even heard it from right-back and I knew exactly what it was straight away.
"Look at Eduardo last week. A nothing tackle has caused him a really bad leg break and he's out for a while. Me, I was nowhere near anyone and I'm out for a while.
"That happens in football. Sometimes you get away with things and sometimes you don't."
Davies added: "It doesn't actually feel too bad. Even at the time I think Roddy Macdonald (Villa club doctor) was quite surprised that I could look him in the eye and tell him that I'd popped my Achilles.
"There's not much pain there, just a few aches where the blood flow isn't quite right. Other than that I'm fine and I just want to focus on getting back."