"Playing in the Premier League is what every footballer dreams about and we've fought so hard to get here, so we'll be working even harder to try and stay in the Premiership, and we can achieve it," said Jackson.
"Every promoted team has to make finishing fourth from bottom their first target, and Wigan will be no different next season.
"Statistically, teams find it tricky because the standard is so incredibly high, but Paul Jewell took Bradford City to the top league and kept them there in their first season, so he will have learned a lot in that respect.
"That vast experience is going to be vital for the rest of us in the coming months because every single game will be a mighty challenge.
"Obviously he is going to sign several players between now and the start of the season, but the manager is a very loyal and fair guy and I'm sure that he will give everybody in the squad an opportunity to prove themselves at this level.
"It is up to us as individuals to see whether we can do it or not."
Latics kick-start life in the Premiership against champions Chelsea at the JJB Stadium on August 13, before Jackson locks horns with Charlton Athletic, one of his former clubs, at the Valley a week later.
The vastly experienced defender has tasted life at the top table with Everton from 1991 to 1997, before his Latics switch four years later.
Jackson added: "The eyes of the nation will be on us when we play Chelsea, and it will be a brilliant occasion.
"Right now, though, the Chelsea game is a long way off.
"First there are new faces to arrive, then we've got to concentrate on our full pre-season work programme, which will be very demanding.
"Really we will only to start to think about the Chelsea game a few days before, because it would be folly to do anything else."
Meanwhile, Jason Jarrett admits leaving Wigan Athletic behind has proved the most difficult decision of his career.
Jarrett, who has signed a three-year deal at Carrow Road, will link up with Norwich for the start of pre-season training on Friday – the day after his Latics contract expires.
"I desperately wanted to play in the Premier League with Wigan, but joining Norwich will probably benefit me more," said Jarrett.
"I will get more opportunities at Carrow Road, but turning down Wigan was the hardest thing I've done since coming into professional football.
"They came back to me twice with a couple of decent offers, and I had the best time of my career there, helping Wigan to two promotions.
"I felt I could have contributed again next season and I know that Paul Jewell had faith in my ability. I was really looking forward to the challenge of being involved with the squad.
"However, I had to think about other factors too, like my family and long-term future.
"I worked with Nigel Worthington when we were at Blackpool together, and when I went for talks it just felt right.
"There was a good vibe there, and looking at the squad they've got at Carrow Road, I really think they can bounce straight back to the Premier League."
Jarrett, a £75,000 deadline-day signing from Bury in 2002, added: "I just want to thank the fans and Paul Jewell for the past few years, because Wigan is a special club."