The Saints keeper allowed a tame Robert Snodgrass free-kick to creep past him just before half-time on Wednesday after Rickie Lambert had given Southampton the lead at St Mary's.
Adkins' side had to settle for a 1-1 draw against the Canaries, but the Saints boss insists he has faith in the 20-year-old and believes Gazzaniga will not allow his mistake to affect him.
Adkins insists the Argentine is destined to become a "top keeper" and has launched a defence of Gazzaniga ahead of Saturday's game at Liverpool, with the shot-stopper set to retain his place in the starting line-up at Anfield.
"I've got every confidence in Paulo Gazzaniga. He is going to be a top, top keeper," the Saints boss told reporters.
"Paulo has got the shirt. He made a mistake the other night but Paulo is great because he is only 20 and he's been big enough to stand up and say: 'Yeah, I messed up there', but it hasn't fazed him and that is the important thing.
"He has a growing confidence about himself and that's an important thing for us. He's got to be allowed to make mistakes so he learns, just don't make the same one."
Adkins is well aware of the pressure placed on Premier League goalkeepers and the Saints boss believes Gazzaniga will continue to improve as the season progresses.
He added: "Keepers are under unique pressures as every situation, every goal, every mistake you make is always going to be highlighted more than the saves you make, because you are expected to make them.
"But as a team I think we have been growing as a team and if you look at all the points we have amassed this season he has been in goal for all of them."