Rangers manager Steven Gerrard had to “rattle a few cages” at half-time before his team eventually swept Hamilton Academical aside on Saturday.
Accies fought back from a goal down to hold Rangers until the final quarter of their Scottish Cup last-16 tie.
But three strikes in the final 22 minutes secured the visitors a 4-1 win and passage to the quarter-finals.
“I was very disappointed in us defensively in the first half,” Gerrard told Rangers TV.
“I had to address that at half-time and rattle a few cages to get them switched on and focused and in the right place defensively.
“Once we did that we played some nice stuff, created a lot of chances and scored some really impressive goals.”
Joe Aribo’s clipped finish, an Alfredo Morelos header and a long-range stunner from Scott Arfield, who had scored the opener, blitzed Hamilton.
Rangers will learn their last-eight opponents on Sunday when the draw is made following the final fifth-round tie of the weekend between Clyde and Celtic.
“The second-half showing was fantastic,” added Gerrard. “We approached it with the right attitude and mentality from a defensive point of view.
“The Joe Aribo goal was fantastic, excellent assist from Ryan Kent. It was nice to see Alfredo back scoring. Hopefully that goal does him the world of good.
“And we save the best until last – Arfield’s strike was a contender for goal of the month, if not goal of the season.”
Left-back Borna Barisic is a doubt for Wednesday’s Scottish Premiership trip to Kilmarnock after the Croat was forced off with a hip complaint in the second half.
“We don’t think it’s a major concern but he’s one that we’re going to have to try and do our best to get out there on Wednesday because he’s so important for us,” Gerrard said.