Flood and Youngs are currently filling bench roles for England in the Six Nations Championship, but they ran the show behind an imperious Leicester pack as Gloucester were destroyed 36-3.
Scrum-half Youngs scored one try and helped create two others, while Flood booted 11 points and kept Gloucester on the back foot through his masterly tactical kicking in miserable conditions.
"Ben and Toby came back to us on Thursday, and we wanted them to enjoy it today and have a crack," Cockerill said.
"We know they are quality players, and I thought they did some fantastic things. Their attitude was really good."
Flood added: "It was great to have 70-odd minutes and to feel amongst it.
"I thought Ben was outstanding. He has been a bit frustrated of late, but he was a real threat. He enjoys running the game."
Five-try Leicester kept themselves firmly in the Premiership title play-off zone after reeling off a 10th successive victory in all competitions on home soil.
Youngs, prop Logovi'i Munipola and flanker Steve Mafi scored first-half tries to underpin Leicester's dominance of a game they controlled in terms of territory and possession, before centre Matt Smith's 58th-minute score sealed a bonus point and an Alesana Tuilagi breakaway effort confirmed the rout.
Leicester toyed with their opponents on the back of rampaging displays by Mafi and number eight Thomas Waldrom. Rarely in the Premiership this season can one side have enjoyed such supremacy.
Cockerill said: "The pressure was on us today - we probably had to win more than Gloucester did.
"It shows that if you have the right mental focus, you can turn things around pretty quickly, and I didn't feel that Gloucester were at the races against us.
"We knew that if we matched them physically, and with the weather conditions like they were, it would probably suit us more than them."
Gloucester head coach Bryan Redpath pulled no punches after seeing his team suffer their heaviest Premiership defeat since leaders Harlequins thumped them 42-6 six months ago.
"We were well and truly beaten," he said. "You have got to turn up and do the basics, but our basics weren't good enough.
"Mentally, we didn't turn up. It does not mean you are a bad team, but we have lost to a side that has always thrived in conditions like that.
"There were some harsh words said at half-time, and we will take the criticism. I want to know why we didn't turn up, mentally."
Gloucester had beaten Quins and Northampton in recent weeks, yet Leicester encountered few problems in putting them to the sword.
"We have got three of our remaining five league games at home, and a lot of dogfights are going to happen between now and the end of the season," Redpath added.
"Today was a great kick in the backside for us. We were second-best in most things, but there is no doubt the next five games are massive."
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