It was a frustrating afternoon at Ibrox as Gers were unable to find the breakthrough against John McGlynn’s side.
From the midweek draw against SC Braga, there were four changes to the line-up as Thelo Aasgaard, Oliver Antman, Nedim Bajrami and Bojan Miovski all came in from the start.
Mohamed Diomande, Djeidi Gassama and Danilo were all named on the bench, with Youssef Chermiti missing out on the matchday squad through illness.
Jack Butland was once again between the sticks, behind a back four of James Tavernier, Nasser Djiga, Emmanuel Fernandez, and Max Aarons.
Nico Raskin and Connor Barron were joined by Thelo Aasgaard in the middle of the pitch, while Nedim Bajrami, who made his first league start of the season, was alongside Oliver Antman and Bojan Miovski in attack.
There was also a return to the matchday squad for Dujon Sterling, who continues his recovery after an achilles injury suffered back in April.
Inside the first five minutes, Connor Barron had a shot held by Scott Bain as Rangers looked for an early opening.
Gers were in control in the opening period, and another opportunity opened up as Max Aarons whipped a left footed delivery deep into the box with Oliver Antman at the back post. The winger got the connection as he headed down towards goal but it was just wide of the target.
Falkirk broke through Calvin Miller as he raced towards goal with five minutes to play before the break, but Emmanuel Fernandez was alert to deny the forward a shot at goal.
Nedim Bajrami came agonisingly close to the opening goal with a fantastic solo effort in the final stages of the first-half. The ball broke to the Albanian at the touchline and he weaved beyond three Falkirk players before curling a right-footed shot towards goal but it was just wide of the target.
Barron flashed another shot wide in stoppage time, as the teams headed in at the break level.
Into the second-half, it was more of the same at Ibrox as Rangers continued to dominate the ball but were unable to really threaten the Falkirk goal.
With 57 minutes played, Röhl made a double change as Jayden Meghoma and Djeidi Gassama replaced Max Aarons and Oliver Antman.
Falkirk were almost able to capitalise as Alfredo Agyeman intercepted a pass from Nasser Djiga to Jack Butland but Gers recovered to deny the visitors.
Agyeman, who had been introduced minutes earlier alongside Scott Arfield, had given Falkirk a lift as he forced a save from Butland minutes later from a tight angle.
At the other end, Nico Raskin played the ball into the path of Djedi Gassama to send the winger through on goal. His shot was matched by a good save from Scott Bain as he got a strong right hand to push it wide, with Bajrami unable to connect with the rebound.
Danilo was next to come on for Rangers with just over 20 minutes remaining as he replaced Thelo Aasgaard.
Ethan Williams forced a save from Butland as the keeper pushed a shot from distance wide from the Falkirk man.
A final two changes followed for Rangers as Findlay Curtis and Mohamed Diomande came on in place of Nedim Bajrami and Connor Barron.
Williams had another shot for the visitors as a clearance fell for him at the edge of the box, but it was just high of the target.
RANGERS: Butland, Tavernier, Djiga, Fernandez, Aarons (Meghoma, 57), Raskin, Barron (Diomande, 75), Aasgaard (Danilo, 68), Antman (Gassama, 57), Bajrami (Curtis, 75), Miovski.
Subs: Kelly, Nsiala, Sterling, Cameron.
Falkirk: Bain, Adams (Hart, 70), Henderson, Graham (Agyeman, 60), Spencer, Allan, Tait, Wilson (Ross, 82), Williams, Lissah (Edwards, 82), Miller (Arfield, 60)
Subs: Hogarth, McCann, Cartwright, Ogunsuyi