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.
By contrast, Reading's immediate return to the Championship was sealed with last weekend's draw against QPR but Adkins sees reasons to be positive.
"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 oversaw back-to-back promotions as manager of Southampton, who sacked him in January, and believes Reading have the right man .
"Having been promoted with Southampton, I know what it takes to go Saturday-Tuesday-Saturday-Tuesday," he added.
"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."