Steven Gerrard acclaimed his Rangers as they could ultimately strengthen their power on the stage.
“It was a very impressive performance, a strong win and another clean sheet,” said Gerrard. “The thing that pleased me the most was the standards that we maintained from start to finish.
“It has been coming, we have threatened to do that. But the pleasing thing today was that we were very clinical. We suffocated Hamilton from start to finish, we stayed on them and never took our foot off the gas and you could see the quality throughout the squad.
Since 1981, the Light Blues did score eight goals in the top flight for the first time. In contrast the Hamilton were beaten 8-0 at Ibrox.
Scott Arfield won Gers in the 16th minute before Kemar Roofe and Joe Aribo ensuing it with two quickfire strikes.
Aribo formed it 4-0 at the break as Roofe got his second score very soon.
“Aribo is a top player. He’s been out for 11/12 weeks so it always takes half of that to get your sharpness back but I think he’s really getting close to that now.
“It was great to get Jermain Defoe a full game today, as it was with Kemar. We’re getting Jermain, Kemar and Aribo really close to full fitness now which is a real help for me.
“You could see flashes against Benfica that his quality was back. And today you saw that when he’s in full flow he’s hard to stop.
The deflated boss said: “Listen, we are down there bottom of the league for a reason. There’s only one way we can go and that’s up. But you’ve got to want to go up and fight.