Jackson was omitted from the squad for the opening day rout by Fulham but fired the opener upon his return in Saturday's 1-1 draw with Queens Park Rangers.
"I came into the team for the match and I want to stay in the team to show what I can do," he told Canaries Player.
"Hopefully my performance will show that. It was also a good team performance and we must build on it.
"We had chances to win in the second half, but it wasn't meant to be and we'll take positives from it.
"You need to win your home games, and I think we created enough chances to win it.
"We'll certainly take those plus points into the next game though.
"I'm delighted to score. We will build on that goal as a team and individually, and carry it on for the season.
"Hopefully we'll get some more results between now and the end of the season."
Newly-promoted Newport has been handed an exciting trip to Championship side Brighton & Hove Albion in the first round of the Capital One Cup.