The Cottagers have survived in the top flight since their promotion in 2001, finishing in mid-table every year and qualifying for the Europa league on two occasions.
In contrast Reading have been condemned to an immediate return to the npower Championship following last weekend's draw with QPR.
"We're not an established Premier League club. We've been in the division and the challenge now is to get back there and have a period of sustainability," Adkins said.
"From that the target would then be to become an established Premier League club. Fulham have managed that and I'd put West Brom and Stoke in the same bracket.
"There might be a situation where you yo-yo a bit between the divisions, that's just being realistic.
"But the structure has to be right and I definitely believe we're on the right lines for that."
Adkins is aware of the challenge guiding a club back into the Premier League poses having overseen back-to-back promotions as manager of Southampton, who sacked the 48-year-old in January.
"Most of the teams in the Championship will have been in the top flight at some point," he said.
"There are some big clubs with big stadiums and good supporters. They all believe they should be in the Premier League. We know how competitive it is.
"Having been promoted with Southampton, I know what it takes to go Saturday-Tuesday-Saturday-Tuesday.
"You must have a squad of players who can deal with the injuries and suspensions that come along.
"And when you do get promoted again you have to be able to sustain being in the Premier League and not make dramatic changes. You have to build gradually."
Striker Jason Roberts has been out since December with a hip injury and Adkins insists he will have a key role to play next season.
"Jason's a player we want to make sure we have fit and available as soon as possible. We'll have to see how the pre-season pans out," he said.
"I thought he was the reason Reading won the Championship. He was a great signing for them. When he came in he scored the goals and kicked the team on."