Downing enjoyed a blistering start to the season, scoring three times in the first seven matches to blast to the top of Boro's scoring charts.
But the England winger received stick from the stands last week as Boro fans rained down the boos during and after the 1-1 draw with fellow strugglers Spurs.
Southgate acknowledged that Downing was not at the top of his game in the Riverside encounter but has no doubt that he will turn the jeers into cheers.
"It's really important that he stays positive," said the Boro boss.
"I've got incredible faith in him and I think there is always somebody that ends up being a target when things aren't going so well.
"All he can do is keep being positive and keep running at people.
"We know the ability of the player. On Saturday he wasn't at his best but he will come through that and he is invaluable to us."