United were controversially relegated from the Premier League last term, as West Ham were not docked points despite breaking rules over player ownership.
And Beattie, who will battle with former Iron forward Billy Sharp for a first-team place at Bramall Lane, insists the side is geared up for a promotion challenge.
"This is a Premier League-quality club and we are perfectly capable of bouncing back at the first attempt, " he said.
"It would be nice to play at Goodison Park again in twelve months time in the Premier League.
"I'm just looking ahead now and looking forward to the new season."