Ally McCoist's men travel to tiny Glebe Park on Sunday (kick-off 3.05pm) for their first competitive outing since being voted into the Irn-Bru Third Division after the club was consigned to liquidation.
The cup clash was given the go-ahead on Friday night when Rangers were granted conditional Scottish Football Association membership.
Second Division Brechin fully expect to head into the match as underdogs, but McCulloch insists the visitors will be taking nothing for granted.
The midfielder told Rangers TV: "Everybody will look at the tie and some will say it'll be a walkover for us but we're not going in with that attitude anyway.
"If we play the way we can, we'll be confident of getting a result but that's all we'll be and we need to work for a win.
"It's not as simple as just turning up and winning. Teams will make it difficult for us this season and they might sit in until we break them down.
"Any time we've played against teams from the lower leagues it has been in cup matches and they've not been easy.
"As such, we're not going into the season with the attitude we're going to win 3-0 or 4-0 in every game like some people are saying.
"The teams in the SFL are going to be very well organised and they'll make it as difficult as possible for us."
Ian Black and Andy Little could both feature as trialists in the cup clash after committing themselves to Rangers on Saturday.
Former Hearts midfielder Black signed a three-year deal, while striker Little has re-signed for two years, with a one year option, after his Ibrox contract expired at the end of last season.
The pair cannot be registered until Rangers' SFA membership is completed next Friday, when the formal transfer of the 'old' Rangers' Scottish Premier League share to Dundee takes place.
The Light Blues are now keen to look to the future following a tumultuous period since being forced into administration in February over an unpaid tax bill accrued during previous owner Craig Whyte's tenure.
Chief executive Charles Green - who fronts the consortium which purchased the business and assets of Rangers this summer - told the club's official website: "This goes all the way back to February and it has been a long, hard road for the fans but now - and we have been saying this for a long time - Rangers is debt-free and no club in Scotland is in that position.
"We even saw the Chief Exec of Celtic out their appealing for Celtic fans to buy tickets.
"We are making the same appeal and what we want to do is to set an example to the rest of Scottish football - particularly the Premier League - that Rangers fans are united and we are walking with our heads held high, taking on everyone in front of us.
"When we consulted with the fans they overwhelmingly said they wanted to go to Division Three and they have their wish.
"We, as a board and investors, said it had no fears for us and we are going to enjoy the journey.
"We'll make a lot of friends along the way, I'm sure, and, while our former friends have the difficulties they are going to face, Rangers and the fans will have an enjoyable few years walking through the divisions.
"We have always believed that the vision we had for the club could be achieved and it's been frustrating that we have had the distractions over bidders that I have talked about before.
"We are not for moving, we don't do about-turns. We have got the club through the most serious challenge it has ever faced and it's onwards and upwards starting on Sunday at Brechin."