The game's key moment came in the 33rd minute when Halsey pointed to the spot after Rodriguez tumbled in the area as Stevens challenged him for a loose ball.
While the furious Villa players raced to question the call, Rodriguez attempted to plead his innocence by mouthing: "I did not dive."
Replays clearly showed, however, that the two players did not touch.
Penalty spot joy and pain
Rickie Lambert has scored all 31 of the penalties (including shootouts) that he has taken since he joined Southampton in 2009
No side have given away more penalties than Aston Villa (six) in the Premier League this season
"We never deserved to lose that," said Villa boss Lambert, "but that is the way things are going for us at the moment. [It] was never a penalty.
"I saw it at half-time on the monitor, and unless you are 100% in a penalty box then you cannot give it. It was evident that was never a penalty.
"Enda [Stevens] is not even close to him. That is the most hurtful thing."
Lambert's namesake Rickie Lambert viewed the incident differently, believing that Stevens's lunge was enough to warrant the decision.
He said: "If I was on the pitch and it was the opposite way round, I would not be moaning about people diving but would be having a go at my defender for making a poor challenge. You have to be careful in those situations.
"I thought it was a penalty. You can clearly see the defender was not going to get there, so that is all I can say."
And while conceding that the two players "probably" had not come together, Southampton manager Nigel Adkins echoed his skipper's sentiments.
Rodriguez did not dive - Southampton boss Adkins
He said: "For me, there is probably no contact, but if the player had not moved their leg away there would have been contact.
"We could have had seven or eight penalties this season - it evens itself out.
"I have looked at it... for me there is no contact with the player. Just as well he moved his foot out of the way, as there would have been.
"All we can do at our place is make sure the players are not diving. We would expect the players to behave properly."
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