Boro slipped to a 3-1 defeat at arch rivals Newcastle to see their faint hopes of beating the drop this season suffer another crushing blow.
The Teessiders opened the scoring early on, as Habib Beye put through his own net, but goals from Steven Taylor, Obafemi Martins and Peter Lovenkrands saw the hosts wrestle three priceless points.
The demoralising defeat leaves Boro three points adrift of safety with just two games remaining.
Southgate accepts things are looking bleak, but feels his team are not getting the rub of the green at the moment.
Anguish"It's been a very difficult evening for us," he said after the derby setback at Newcastle.
"There is a lot of frustration and anguish in the dressing room because it's such an important game, the type of which many of my players have never experienced before, and to lose it in the manner we did is very difficult for all of us to take.
"It's a tough evening for everyone connected with our football club. From the fantastic fans that travelled and made such a lot of noise, to the players who gave everything, but unfortunately key events on the evening have gone against us.
"I thought we were competitive throughout the game and there looked to be very little between the teams.
"Realistically, though, the second goal, which changes things, the ball bounces perfectly for them and they were able to take that chance."