Trailing by six points in the closing minutes of the Pool Two clash, it looked as though the Aviva Premiership side were heading out of Europe as Treviso got ready to celebrate a famous victory.
However, a series of scrums on the home line led to a penalty try and the subsequent conversion by George Ford ensured the former champions lived to fight another day.
"We're obviously very relieved because we came away with the win," Cockerill said. "You have to congratulate Treviso for the way they played. They made us work exceptionally hard.
"Conversely, you have to congratulate our players for sticking in there and digging in right until the end.
"Everything went against us really. We scored a really good try in that first half, but somehow we upset the referee and he was against us for a fair bit.
"You could easily let all those factors get on top of you and throw in the towel. But we didn't, we stuck to our guns, played for the win, and eventually we got it."
Despite the late penalty try, Cockerill's annoyance with referee Alain Rolland was palpable during his post-match interview.
His main gripe was over a penalty try awarded to Treviso midway through the first half.
At the time the Tigers were leading thanks to a magnificent 14th-minute try by Adam Thompstone, but were rocked on their heels when Rolland bizarrely pointed to between the posts for an infringement at a maul 13 metres from the line.
"I don't know if I'll ever see a more bizarre penalty try," Cockerill added. "I have never seen anything like it in the 30 years that I have been involved with rugby. I was just amazed.
"If that had been awarded for us I would have sat in my chair in embarrassment."
Treviso coach Franco Smith did not quite understand what all the fuss was about.
"It's not my style to criticise referees," the South African said. "Maybe he was right, maybe he wasn't.
"If you look at the game as a whole you could reference numerous occasions on both sides where incorrect decisions were made. But that's part of the game."
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