Highlighting the club’s stature and support base, the Northern Ireland international insisted last season’s achievement can be the start of something big at Bramall Lane.
Over 31,000 people watched Chris Wilder’s squad sign-off a remarkable campaign in style by beating Chesterfield 3-2 on Sunday.
Lafferty, previously of Celtic and Burnley, said: “Listen, a club this size should be successful, especially with the fans we’ve got here. The backing the club has is outstanding. It should be up there contending for honours all the time.”
United sealed their return to the Championship following a six year absence last month before a run of seven straight wins saw them finish the campaign on 100 points; 14 clear of their nearest rivals.
Lafferty, who scored the decisive goal against Gary Caldwell’s side, moved to South Yorkshire in August and said: “This club probably should have gone up much sooner. But, for whatever reason, it’s been six seasons.
“Every year, we’ll have been one of the favourites. But, until now, we’ve not got over the line.
“Like the manager says: ‘football isn’t always like this.’ So we’re just going to really enjoy it when we kick our boots off. We can put our feet up and enjoy it and, to be fair, I think it’s important we do that. Then it’s back to it and getting ready again because we do drive ourselves on all the time.
“To get the final goal of the season was nice. But, to be fair, it’s not about individuals. It’s about the group as a whole on and off the pitch. Because we couldn’t have done this without each other.”