There is a welcome buzz around the city at the moment, following the south Wales side's final day promotion, and the imminent move to the new stadium at Morfa.
"I'm not saying it's going to be easy - this division is a lot tougher than the one we've just come out of - but our ambition is definitely to win promotion. That's what we're working towards.
"There are some very good sides in the division and we've got some tough trips up north to deal with.
"But there's no reason why we can't be competitive. The other teams might be worried about coming down to
"There's never anything to fear in football. We're in a harder league, but I think there's everything to play for," he added.
"You can write down now who will be the top five in the Premier League, but you can't do that for League One and League Two.
"There are always surprise elements in those two divisions, and I feel that gives us a chance.
"Look at the sides who won promotion to League One last year.
"To me that suggests it's an open field and that there's a hell of a lot of room for manoeuvre.
"If you go back 12 months nobody was saying
"I remember looking at the bookies' odds and we were about halfway. Teams like
"It was a varied field and I think it's a similar situation in League One."
A quick look at the latest League One odds for the new season, and one is not surprised to see that the Jacks are not favourites to go up
You can get a rather tasty 25-1 for a Swansea promotion, while Notts Forest are favourite at 4-1, with Tranmere at 8-1 and Bristol City and Huddersfield both 9-1.
"You can say we only squeaked out of League Two, but, at the same time, we only finished three points off the top," said Jackett.
"I've got make sure we go into this league and compete. We can't come into it and be second-best. I don't want us to be overrun.
"I think we will have a surge of impetus because we're in a new division and playing in a new stadium.
"But I want a squad that can compete in the top half of the division."
Jackett is still on the transfer hunt, making clear he feels four players could strengthen his squad and make them on of the better teams in the league.
Jackett is still keen on Bristol City's Marc Goodfellow, while he is also mulling over improved bids for Rochdale's Grant Holt and Rushden's Andy Burgess, however, the boss has said he may go elsewhere if his prime targets aren't possible.