Brazil international Oscar chose to forego an almost certain goal at St Mary's when he went tumbling in the box as he attempted to round Davis in the second half with the score still at 0-0.
Referee Martin Atkinson booked Oscar for simulation and Chelsea manager Jose Mourinho admitted he deserved the caution.
"He didn't need to do it," said Davis.
"If he went around me, he would have popped it in the net. I think it is probably a habit of his that he felt he had the opportunity to win a penalty and, for me, he probably looked too hard for it and that is why the decision went against him.
"I was happy that he (Atkinson) spotted that as I have seen them given.
"I don't like that because I could have ended up getting sent off on the back of it.
"For the referee to spot that is good. I am not concerned about him getting booked, just avoiding the way the incident could have gone."
Oscar went on to score Chelsea's third goal as they wrapped up a 3-0 win to leave Southampton with only one victory in their last nine matches.
Saints' poor form has led to further speculation that some of their leading players could be sold in January but Davis is not expecting any departures.
"We have a passionate chairman who is very keen on keeping everyone at this club," he said.
"He rewards the players very early on in their careers and I think the players respect that and that is why when the opportunities come along they hold off until the right time, if at all.
"I have been in the situation at many clubs. Since the Liebherr family and Nicola Cortese took over, the mentality of the club has changed.
"If the player wants to leave, the club make the decision if they can or not. When they want to bring a player in the resources are there to do that."