Newly-promoted Millers have adapted well to life in the second tier despite operating on a budget dwarfed by most of their rivals in the division.
But Rotherham have been guilty of dropping some valuable points in the opening third of the campaign, like conceding a late penalty to lose at Nottingham Forest and blowing a 2-0 lead to draw with Stoke City. Fourth-from-bottom Rotherham are just five points adrift of mid-table Sheffield Wednesday underscoring to Warne the fine margins between success and failure.
“I think realistically most people find their way by this stage,” Warne said.
“But I still think we should be four or five points better off than where we are at.
“We should be on level points with the likes of Villa and Brentford, which is impressive.
“I don’t see us as a bottom-six team, I definitely don’t, and nor will I let the lads think like that.
“The top eight are breaking away, but as the cliches go it is a long, hard season and there are some tough months coming up.”
The Millers have lost just once in their last six outings, an impressive run in a fiercely competitive Championship.
But the other five games have all ended in draws meaning Rotherham – who were relegated two seasons ago with just 23 points – need to start winning again quickly if they want to climb the table.
“I haven’t found it easier because every point or three points you get is a bloodbath,” Warne said.
“Everything is a struggle. I just think the lads have on the whole done exactly as we’ve asked.
“The performances have been as close to the best we can be, any team can beat any team.
“We have had to make every game a cup final. I wouldn’t say it’s been easy by any stretch of the imagination, there is always a part of me that thinks we could lose the next five games, we could win them as well.
“I feel like the lads have given everything and we are still where we are. I have a fear of that, I look at the league table like everyone else,” he said.
“I just think the lads have surprised a few teams. However, when we play those teams on the second lap they won’t be surprised any more, which is why we need to pick up points as fast as we can.”
Swans manager Graham Potter – a former York City player who had spells working at Leeds Metropolitan University and University of Hull – has been impressed by Rotherham.
“They are doing really well with what they have,” said Potter.
“They are well-organised, they play to their strengths and they are dangerous.
“They have a great team ethic, are well-coached and have a clear idea of what they want to do.
“You can see how they can take points and win football matches,” he added.
“I have been really impressed with them in the games that I have watched and this is going to be a difficult game for us.”