The Iron were relegated the last time they reached the second tier but made an instant return after winning the League One play-off final in May.
And despite them having the lowest playing budget and average attendance in the division, Adkins is refusing to accept that relegation is a foregone conclusion.
"We might have the lowest crowd in the Championship and we might have the smallest budget, but that does not mean we should not aim for the highest standards," he told the Scunthorpe Telegraph.
"The last time we reached this level we came straight back down - and there is no way I want that to happen again.
"We have got to aim to be the best we can. We have got to have that winning mentality and aim to finish as high up the table as we can. We were little old Scunthorpe before - but we are not now."