After tries from Croft and Keenan Palasia, Sivo claimed the ball from under his own posts and ran 70 metres for an attack which ended with Ryan Hall scoring.
A Hull KR try was disallowed for an earlier obstruction before the end of the first half, but Leeds continued to dominate in the second period – with Croft adding a sixth try before Sivo completed his hat-trick.
His fourth try came after a Joe Burgess consolation for the Robins 15 minutes from time – then a late Cooper Jenkins double sealed a resounding victory for Leeds.
“The people I feel sorry for are the fans who paid hard-earned money to come here today and watch that,” Peters said.
“To spend or save money to come and watch their team play and we deliver a performance like that, it’s just nowhere near good enough.
“We need to all look at ourselves – myself at the top of that – and find out why we got that performance.
“We need to make sure that we action more than words and do something about it, because if that’s the template of what we’re going to do this season, it’s going to be a long season.”
A delighted Leeds coach Brad Arthur said his side had “had a ball” and praised his players’ “real hunger”.
“We wanted to make sure that we did ourselves proud and the fans and did the competition justice,” he added.
“We came here to make a statement and we did it tonight,” Sivo told Sky Sports.
“The boys, every single one of us, did our job tonight.”