The 18-13 triumph kept Tigers in touch with the top four in the Aviva Premiership table and was gained without more than a dozen senior players unavailable due to international calls or injury.
Cockerill said: “With the guys we’ve got missing and the confidence Quins had from their win here in the cup two weeks ago, that was a vital win for us. It’s important we enjoy it because we’ve had a couple of tough weeks.
“Quins thought there was a bit of vulnerability in the camp with the people we have missing, but we had just enough about us to win the game.
“We had to just dig it out and that is what Leicester Tigers do.”
Tigers went behind to two early penalties from Nick Evans but led 18-6 before a last-minute score from Tom Williams gained the visitors a losing bonus point from the Round 8 clash.
“I’m delighted with the character of the players,” added Cockerill.
“We needed to dig it out and play the game in the right areas. Billy Twelvetrees kicked his goals well, our defence was good, and the spirit and the willingness to really dig in and really roll up our sleeves was key.
“In the context of the season that is an important win for us.”
Cockerill pointed to the efforts of props Peter Bucknall and Julian White, and the back-row unit of Thomas Waldrom, Craig Newby and Jordan Crane as typical of the squad’s commitment.
“Pete came in to do a job, he wanted it, he stuck at it, and Whitey is extremely good at what he does,” Cockerill said.
“He’s been on the farm all day then plays in a game like that. That kind of enthusiasm is great for the club.
“They all want to play for the club, they know how important these games are when we have players away with international squads.
“The work-rate of Thomas and Jordan was really important and I thought Craig Newby in the back row was outstanding.”
The only blemish on the evening was an injury to lock Geoff Parling in his first appearance of the season.
Parling had not played since England’s summer tour due to a neck injury and, after coming through months of recovery work, he was introduced as a second-half replacement, only to suffer a knee injury moments into his return.
“It’s too early to know exactly what he’s done,” said Cockerill. “Geoff will have a scan and we’ll go from there. Let’s hope we’ve not been cursed by injury again.”
