Despite being top try scorers in the division last term, all-firing Ospreys suffered a 30-27 defeat to Zebre in May and subsequently finished outside of the top four.
This season's trip to Parma was not quite as harrowing, as Sam Davies kicked five penalties to secure a 15-14 victory.
Saturday's 26-12 win over Munster Rugby moved Ospreys up to fourth in the GUINNESS PRO12 table, but with the season nearing its climax and their play-off aspirations on the line once again, Tipuric is fearful of another slip up against their chief tormentors.
"We know what Zebre can do," Tipuric told Ospreys' official website.
"This result [v Munster] will mean nothing if we don't follow it up against Zebre, so that has to be the challenge, to find the consistency needed.
"It's not a year since they turned us over and we only won by a point out there at the start of the season, so we'll have to perform to this level again or what we've gained in this game will be wasted.
"We've got five games left now, they aren't easy, and each one of them is vital if we are going to finish the season where we want to be."
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