كتب : Ahmad Saied
Boro, who missed both Egyptians Ahmed Hossam 'Mido' and Mohamed Shawky, grabbed the opener in the 79th minute through a Tuncay Sanli strike.
But Hull responded quickly as Bernard Mendy and Marlon King scored to secure the three points.
King notched the winner from the spot after Geovanni was brought down inside the box but Southgate believes the penalty shouldn't have been awarded.
"Obviously the winning goal is pretty questionable," he said after the game.
"I think the pictures clearly show he (Geovanni) is offside to start with. He is coming back from an offside position and that gives him an advantage."
The former England defender also said that David Wheater's challenge was "pretty soft" to be called.
"We should have defended it instead of appealing," he said.
"But then it just looks pretty soft and when I think about the other decisions given throughout the afternoon, for them to get a decision in that area of the field I find very surprising.
"But we can do nothing about that. We have lost the game and we have to take our medicine."
Middlesbrough are now just four points above the relegation zone. They have 19 points in the 12th place.