Nir Bitton claims "everyone" wanted Celtic to fail before they recovered from their Old Firm defeat to storm 13 clear at the top of the Premiership.
A 2-1 win at Celtic Park on 29 December took Rangers to within two points of the holders with a game in hand.
But, as Steven Gerrard's side have slipped up, Celtic won eight league games in a row before Wednesday's 2-2 draw away to Livingston.
"Everyone wants to stop us, they want to beat us," midfielder Bitton said.
"I think, after the Old Firm game before the winter break, everyone killed us, everyone wanted us to fail. Every away game in the Scottish league is difficult and, to be the hero, we need to accept it, we need to face it."
Even Rangers captain James Tavernier and manager Steven Gerrard have admitted that Celtic's city rivals have failed to cope with the pressure of preventing Neil Lennon's side achieve a fourth consecutive clean sweep of domestic trophies.
"When you play for a club like Celtic, you have to believe all the time," Israel international Bitton said. "You play for a massive club, you're always fighting for trophies, you have to have this winning mentality.
"Every game, even if we are down, even if we are up, we play the same style of play. We will always be on the front foot and try to win the game and it's a special dressing room to be in."
However, Bitton insists a ninth domestic league title in a row is not already secured.
"We were very disappointed to drop points on Wednesday night," he added. "We gave away two goals that put us under pressure for no reason.
"We need to cut it from the next games and need to make sure that we win the league as soon as possible.
"It's a long way to go - still nine games and 27 points is enough points to try to close the gap. We need to make sure it's not going to happen."