The Italians found themselves rock bottom at the end of last season after losing 15 of their 22 matches.
That is a record that Bortolami believes his team can better this time around and the former Italian skipper is eyeing an ascent up this year's league table.
Zebre picked up five wins during their last campaign and one of those came against Cardiff Blues who will travel to Parma for the opening round of fixtures.
It is a match Bortolami sees as winnable but, while he thinks his side have strengthened over the summer, he knows that other teams are in a much better position as well and is expecting to have to fight for every point.
And the key to winning those battles is a solid defence and a resilient attitude that makes Zebre a difficult proposition for any side.
"We are positive but I think that the other teams are better than last year. Cardiff are definitely better and much stronger. Dragons are much stronger than last year as well so the mid-table teams are in a better position," he said at the official season launch.
"We had a couple of friendly games against some Italian sides which were not too difficult so I think the first game against Cardiff is going to be very interesting to see where we are and if we are in the same position as we were last season.
"It's very important to start with the right structure and hopefully we can win the first game of the season.
"The question is we have to be ready as individuals and as a team from game one, that's the big challenge.
"We have to be hard to beat, that's the basic point. Apart from that we can score tries and we have got some exciting players."
With a host of new additions joining Zebre this summer Bortolami is excited about the big kick-off and believes the Italian outfit will be able to claim a few unexpected victories over the course of the season.
"We are very excited about the new season, it's been a good summer for us. We had a few new players coming in so we start from a good point," he added.
"We want to make a mark on the league and we don't want to finish bottom again. The way we do that is important and we want to be competitive in every game.
"Last season our first win was in Cardiff away so it was a magical win and unexpected so chances will be there this season as well.
"We could have won against Ulster as well so I think we don't have to focus only on home games we have to play with consistency week in week out.
"Sometimes we give away too many soft tries or soft penalties and that's where we need to improve.
"We have to be better than the opposition in that way and be disciplined and make sure we don't give away points."
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