Replays indicated that Villa defender Enda Stevens made no contact on Rodriguez before he went down in the area.
But referee Mark Halsey - a late replacement for the ill Chris Foy - thought otherwise and Saints skipper Rickie Lambert made no mistake from the spot for his ninth goal of the campaign.
Adkins said: "I've seen the video. The challenge on Jay, there is no contact.
"Jay's leg has moved out of the way which is just as well otherwise there would have been clear contact.
"We don't advocate diving at our club and we probably should have had seven or eight penalties this season we weren't given.
"It is a big decision. It is not a dive."