However, but for two fine first-half saves from Mark Schwarzer to deny impressive Stags striker Michael Boulding, the Teessiders could have endured a far less comfortable afternoon in Nottinghamshire.
Southgate was a happy man after seeing his team avoid a potential upset on a tricky afternoon.
He said: "It's the FA Cup, isn't it? When we were travelling down yesterday and there were lorries blown all over the A1, you think, 'Yes, it's FA Cup weekend'.
"I never feel pressure in the cups - I know perhaps you should when you are playing lower division sides but I always think the cup is something different, away from the pressures of the league.
"It was the same when we went to Bristol (in the last round) - you are always on a hiding to nothing. All you can do is try to win the game.
"I don't think we played as fluently as we might have done but we were very strong at the back.
"We knew Mansfield would at times be quite direct and the back four would be in the game all the time.
"We caused ourselves a few problems as the game went on and made it harder for ourselves than it might have been.
"But great credit to Mansfield, they pushed us all the way and I guess they played the way you would expect a lower division team to play in a cup tie like this. They gave it absolutely everything."