The summer signing from Birmingham City scored with a stunning chip past City goalkeeper Ederson.
Adams came close to leaving in January but manager Ralph Hasenhuttl insisted he wanted the Englishman to stay.
Quizzed on whether he had re-paid Hasenhuttl's faith to keep him in January, Adams replied: "Yeah.
"There is a lot of competition in the forward areas and to score means a lot to me. Hopefully we can keep going now.
"I want to grow in confidence and get as many points and minutes as I can."
Adams added that he would like to help the Saints make it three wins from three against Everton on Thursday.
"That's the aim. We want to pick up three points in every game and we managed to do that against Man City.
"We want to carry this on into the game with Everton on Thursday."