Martin O'Neill warned Celtic face a "big, big fight" to retain the title after he returned for a third spell as manager.
The 73-year-old has replaced the sacked Wilfried Nancy 33 days after making way for the Frenchman following an interim spell in which he won seven out of eight matches.
O'Neill left Celtic level on points with William Hill Premiership leaders Hearts with a game in hand and nine ahead of Rangers.
They are now six behind Hearts with the same number of matches played and will be three points off Rangers in third if the Light Blues beat Aberdeen at Ibrox on Tuesday.
"We know that we're in a fight," O'Neill told Celtic TV.
"We're in a big, big fight.
"We're going to try and win the league. It'll not be easy. It never is, regardless. You set out way back at the end of July, beginning of August time, started off trying to win. The season before that, you put that to the side at the time.
"But now we're halfway through the season, and we've a fight in our hands, a big, big fight. And so we have to be up for the challenge. It is tough."
O'Neill faces an even bigger challenge than he did when dealing with a squad who were in shock after the departure of Brendan Rodgers.
They lost six out of eight matches under Nancy, whose system seemed to cause confusion and defensive vulnerability.
"I used this phrase, restoration of confidence, way back when I came in first of all," O'Neill said. "And I suppose that would probably be a similar message again.
"The lovely thing about it is that when players that you know are very fine footballers can come back and perform to the standard that they have done in the past.
"And if all of those things fall into place, then you've got a chance of winning."
O'Neill has been installed until the end of the season.
"That conversation with (principal shareholder) Dermot Desmond was one that I think maybe might go through to the end of the season, giving the football club time to really look around, get someone in who's going to be here for the next three or four years," he said.
"But listen, I'm in the football business. I might not see it through to the end of the season. You know, you have to win football games."
O'Neill, who appeared to be back at Celtic Park already, admitted it was surreal to have returned yet again, but stressed his sympathy for Nancy.
"It is a mad, crazy football world," he said. "You're absolutely right. You know, just at this minute, because it's happened so quickly, I really don't know what to say.
"I'm obviously very, very pleased, privileged to be back again at the football club.
"Before, Brendan had resigned and therefore there was that small opportunity to come back to the football club.
"But in circumstances as this here, with Wilfried leaving the club, that just seems a wee bit strange just at this moment.
"I'd been there before as a young manager as well, coming into a strange, strange environment, coming into something here that you think that you know about.
"I grew up knowing about Celtic Football Club, but way back in 2000, when I arrived, I really did not realise just how big the football club was and what it meant to people as well.
"He will be successful again and he'll have learned an awful lot."
