Martin’s men were reduced to 10-men after a Max Aaron’s red card early in the match, as the Belgian side progressed to the league phase of the competition.
From last week’s first-leg there were two changes with Lyall Cameron and Thelo Aasgaard coming in for Nico Raskin and Mohamed Diomande. Jack Butland was once again in between the sticks, with a back four of Jack Butland, Max Aarons, John Souttar, Nasser Djiga and Jayden Meghoma.
Joe Rothwell, Lyall Cameron and Thelo Aasgaard were in midfield, while Danilo led the line with the support of Oliver Antman and Djeidi Gassama.
With five minutes on the clock, it was the home side who increased their advantage in the tie. Joaquin Seys picked the ball up down the left and whipped the ball into the box which Nicolo Tresoldi headed beyond Butland.
It went from bad to worse for Rangers with just eight minutes played as Max Aarons received a straight-red card as he brought down Christos Tzolis as he raced through on goal for the hosts.
That red forced Martin into an early change as captain James Tavernier was introduced in place of Oliver Antman.
Jack Butland pulled-off a good save on 19 minutes as he reacted well to a close range effort from Christos Tzolis. The hosts were really pushing for a second-goal and Tzolis rattled the crossbar with a looping strike from outside the box.
The Rangers goalkeeper was called into action again as he stood strong to block a goal bound effort from Carlos Forbs with his feet.
From a corner, which was swung into the box by Christos Tzolis, captain Hans Vanaken rose highest and glance beyond Butland to increase the Belgian sides advantage. Just minutes later Hans Vanaken hit the bar with a right-footed strike as the relentless pressure from the home side continued.
With five minutes of the first-half remaining it was 3-0 to the home side on the night as a ball was delivered into the box by Kyriani Sabbe. Joaquin Seys' initial strike was blocked by Butland but he followed up the rebound.
Another one followed before the break for the Belgian side, and it was another for Joaquin Seys. This time the delivery came from Raphael Onyedika to the back post and the full-back finished beyond Butland.
It was relentless from the home side, and it was 5-0 in added time, another ball into the box caused problems for Rangers and Aleksandar Stankovic headed beyond Butland.
There were three changes at the break for Rangers as Nico Raskin, Mohamed Diomande and Findlay Curtis were introduced in place of Thelo Aasgaard, Joe Rothwell and Djeidi Gassama.
Less than five minutes into the second-half there was another for the home side as Christos Tzolis sent a shot into the far corner of the net after getting on the end of Nicolo Tresoldi’s ball. Connor Barron was introduced as the final change for Rangers as he replaced Danilo.
Butland pushed away another shot from Aleksandar Stankovic inside the final 20 minutes, as the home side controlled the remainder of this tie.
RANGERS: Butland, Aarons, Souttar, Djiga, Meghoma, Rothwell (Diomande, 46), Cameron, Aasgaard (Raskin, 46), Antman (Tavernier, 11), Gassama (Curtis, 46), Danilo (Barron, 59).
Subs: Kelly, Wright, Dessers, Fernandez, Moore, Gentles, Hutton.
Brugge: Mignolet, Tresoldi (Furo, 68), Tzolis (Nilsson, 58), Forbs (Diakhon, 46), Onyedika, Vanaken, Stankovic, Mechele, Spileers, Sabbe (Audoor, 72), Seys (Siquet, 58)
Subs: Jackers, Romero, Reis, Vetlesen, Sandra, Meijer, Skóraś.