Celtic are more used to being front runners, but heading into Wednesday’s game away to Aberdeen, they lie third, eight points adrift of Hearts, two behind Rangers, albeit with a game in hand over both, and only two ahead of Motherwell.
“It’s probably exciting if you are watching it from the outside,” Tierney admitted. “It’s probably something that’s not been there for a while.
“It’s massive, but regardless of the situation, every week the game matters for Celtic.
“It’s not new to us. Maybe the situation is, with three or four teams going for it, but the pressure of playing for Celtic is not new to us.
“But we are focusing on ourselves, not the teams around us.”
Having come from two goals down to draw Sunday’s Old Firm derby away to Rangers, with Tierney scoring the visitors’ opener, Celtic head to Pittodrie with the chance to overtake their city rivals in a “positive” frame of mind.
Tierney says O’Neill’s squad are trying to work out why they have made so many slow starts in recent games but are also looking to build on “the determination and the character that we showed – and the quality we showed as well” in the second half at Ibrox.
The Scotland defender thinks “it would be massive” to move above Rangers but stresses that, despite the eighth-placed hosts’ recent poor form, “Aberdeen away for any team at any stage of the season is a hard game”.
He recognised there is room for improvement in Celtic’s performances if they are to win the title and added: “You can’t just rely on resilience and character. We need to show we can play as well.”