The Croatian international left-back admits the Ibrox club are finding it tougher to retain the title than it was to win it for the first time in a decade.
Rangers recorded three wins and a draw against Hibs on their triumphant march to become champions last season but all three victories were by a single goal in closely contested fixtures.
Barisic believes Jack Ross’ side, just a point behind Rangers ahead of Sunday’s visit to Ibrox, have improved since then.
“Hibs have shown this season that they are a very good team,” said Barisic. “I think that they have shown, even in previous seasons, that they play good football.
“But this season, they have been a little bit even better so it will be a very interesting game.
“The table shows that it’s possible (they are challengers). They are playing very good football this season and they are very close to us, so of course. Why not?
“You know, when we became champion last time, it’s not easy to stay there. They say it’s easier to climb a mountain than to stay there. But that’s what makes you a champion, right?
“When you put the standard so high like we did last season in every aspect of our football game, then of course expectations are very big.
“But that’s what makes you a champion and is the difference between someone who can do that for one season or someone who can do it a few seasons in a row, someone who has consistency. That’s the thing we’re trying to find and what we want to achieve this year.”
Rangers face Hibs on the back of another disappointing Europa League defeat against Sparta Prague which left them pointless at the bottom of Group A after two rounds of fixtures.
“We didn’t start very well, we lost two games,” said Barisic. “But we showed last season and the season before that we have the capacity to play good football in the Europa League. We will try to do that this season.”