The Bairns play host to Ally McCoist's men in the Ramsdens Cup on August 21, before travelling to Ibrox for the second round of the Scottish Communities League Cup - which was drawn at Hampden today - a week later.
Shiels helped Kilmarnock claim the League Cup last season and is hungry for more silverware with his new club.
But he is well aware of the dangers posed by Falkirk, who dumped Rangers out of the competition last term.
He told www.rangers.co.uk: "It was great for me to win it last year, it gives you more hunger and desire to do it again.
"But we won't be looking too far past Falkirk and we need to take it one game at a time.
"Falkirk had a good season last year and Steven Pressley has done a good job there.
"But I think for any cup tie you want a home draw so we look forward to that.
"It's going to be very tough and we've drawn them in the Ramsdens Cup as well so we're going to be very familiar with them.
"I think they pass the ball well, they're young and they're keen to do well.
"But in front of our fans we will want to go out and do well.
"Hopefully this can push us on to a cup run."
Shiels made his debut in Tuesday's 4-0 win over East Fife in the first round after signing for the Ibrox side last week.
He added: "It was an honour to make my debut and to play for the club.
"I am delighted to be here and I'm delighted we got off to a great start.
"On a personal level that was only my first game for three months and I think it was only the second game for a lot of the lads.
"So it's going to take four or five games. There's been a big turnaround in personnel so it's going to take a while for us all to gel.
"But hopefully you'll see the best of us in the coming months."
Meanwhile, Scottish Football League chief executive David Longmuir believes having Rangers in the Irn-Bru Third Division will provide a boost to the other clubs.
He told RangersTV: "I think having Rangers in the league now will create awareness and will bring a new vitality to the Third Division.
"I know it's probably not the place that Rangers want to be and probably shouldn't be but, nevertheless, that's the way Scottish football has handled this situation.
"Having been at Glebe Park last Sunday to see the Ramsdens Cup tie, I thought Brechin put up a great show and Rangers were a wee bit rusty.
"But it was more to do with the buzz and excitement that having Rangers in town brought and I hope Rangers fans will be welcomed like that wherever they go in the SFL.
"All 10 clubs in the Third Division will benefit from having Rangers there.
"Attendances will be terrific, albeit only on a couple of occasions each season at each ground."
The Rangers Supporters Assembly tonight echoed McCoist's call for fans to back the club and buy season tickets as the Glasgow giants continue on the road to recovery.
Assembly president Andy Kerr said: "The response from fans already this season has been extraordinary and the fans are central to the club's recovery and our support will take us forward and help propel us back to the top.
"There has already been a great response to season ticket renewals and many are waiting to become new season ticket holders for the current season.
"The fans have been magnificent for years now and even more so in this period of uncertainty and we urge them now to back the club by buying season tickets to assist the club to move onwards and upwards.
"The signs are positive and it is great that so many fans are united behind Ally and the team.
"This last six months have been pretty horrendous for all Rangers fans and it is helpful that we are now playing football again, focusing on winning football matches and cheering the team on as we've always done.
"There are still off-field issues to be dealt with and they will take their course, but the fans can now look forward to a Rangers team competing for honours."
