Craig Bellamy, who joined City from West Ham in the transfer window, scored the only goal of the game.
Southgate has urged his side to keep the belief that they can manage to stay in the Premier League.
“I’m disappointed we’ve not won again – we’ve done so many things right and it’s frustrating,” Southgate told Sky Sports.
“We looked solid and created chances away from home and not finished them, it’s as simple as that.
“Performances like that are the reason we are where we are (in the table).
“We folded at Fulham and West Brom but today we’ve done pretty much everything right.
“We haven’t finished our chances but we’ve created them and we’ve got to maintain the belief we can do that (survive).”
