The visitors, who are still to win on Irish soil, held an 8-3 half-time lead after Hennie Daniller's try and a penalty from Mirco Bergamasco.
But O'Connor's men responded with four unanswered second-half tries, with fly-half Jimmy Gopperth adding to his score by kicking nine points in an eventual 29-8 bonus-point victory.
"There is a lot of things that we can be better at. The learning will be steep but it has to happen by next Friday," said O'Connor, whose side next travel to Ospreys in the GUINNESS PRO12.
"We had several opportunities to score in the first half that we didn't take, that kept them in the contest and kept them semi-interested.
"The second-half performance was a little better but there were a lot of errors that played into their hands and their ability to slow the game down."
Gopperth's 32nd-minute penalty was all the defending champions had to show for their first-half efforts but came out firing after the break.
After Luke Fitzgerald burst through the Zebre defence and was stopped just short, Dominic Ryan touched down on 46 minutes before Gopperth added the extras to give Leinster the lead.
New Zealander Gopperth added another seven points ten minutes later, when the returning Eoin Reddan fed the fly-half from the base of the scrum, for Gopperth to step inside and finish.
With 74 minutes on the clock Fitzgerald finished in the corner to all but seal the victory after patient build-up from the much improved hosts.
And with the last play of the game a fourth try was added, and the bonus-point secured, when Sean Cronin scored before Gopperth added the extras.
O'Connor praised the roles played by Fergus McFadden, Fitzgerald and Dave Kearney and said he expects them to feature for Ireland again before long.
He added: "They're test standard players and they will be in the mix pretty soon.
"Ferg, Luke and Dave are very, very close to being in the mix.
"I wouldn't be surprised if there are injuries over the next couple of weeks with Ireland, that those blokes will be playing."
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