Boro had led through a Tuncay goal on 79 minutes but Hull were back on level terms a minute later through substitute Bernard Mendy.
Three minutes later came the incident which infuriated Southgate as Wheater was shown a straight red card by referee Steve Tanner for hauling down Geovanni in the area and the hosts scored what proved to be the winner when Marlon King slotted home the resulting spot-kick.
"A draw would have been a fair result. When you go ahead at that stage you expect yourself to win it," Southgate said after the match.
"Obviously the key was keeping that lead longer than we did, but we were naive in the way we played that 90 seconds.
"The penalty was extremely harsh especially given the fact that the pictures clearly show that he (Geovanni) is offside to start with. He is coming back from an offside position and that gives him an advantage.
"We can do nothing about the referee's performance. However it is a bitter pill to swallow."