Goals either side of half-time from summer signings Joe Aribo and Sheyi Ojo gave the dominant hosts victory.
But Gerrard bemoaned a stack of missed chances that gives the Luxembourg side hope in the second-round qualifier.
“I’m frustrated we didn’t score more,” the Rangers manager said.
“We created enough on the night – you can see there was a gulf between the teams – but we haven’t got the rewards our performance deserved.
“We need to be more clinical to put these teams away because I really wanted to kill the tie tonight.”
James Tavernier hit a post with a second-half penalty and Ojo and Ryan Jack had goals disallowed as Rangers sought to exorcise the ghosts of their embarrassing exit to Progres two years ago.
But the home side had goalkeeper Allan McGregor to thank as Progres came close to grabbing a shock away goal when substitute Jack Mmaee broke clear with 11 minutes left.
“Obviously the penalty springs to mind and we probably had six or seven decent chances on top of that to score more goals,” Gerrard added.
“As the game goes on we’re chasing that third goal and lose a bit of discipline and shape at the back and we could have been caught out. Again Allan came big for us but that’s no surprise as he’s a top cat.
“There’s still a lot of work to do to kill this tie off.”