Celtic boss Ronny Deila's contract at Parkhead is due to expire at the end of the season.
Deila has come under pressure at Parkhead, with many of the Bhoys’ supporters suggesting that he has not advanced the club.
Celtic have failed to impress in Europe under the Norwegian’s stewardship, and they have put in a number of questionable performances in domestic action this term.
Despite this, Deila still delivered the double at Celtic last season, and the Glasgow side look on course to win the Scottish Premiership again this term.
And Smith said: “I think Ronny Deila has had kind of a rough ride, but he has not had the motivation that Rangers bring to the league championship.
“Any assessment you have to make on Ronny Deila is a difficult one. They have dropped a little bit of a level, maybe quite rightly, because they don’t need to spend the money that had to if Rangers were challenging them for that Champions League place.
“I think Celtic have downsized a bit, which has made it more difficult for Ronny Deila.”
Deila’s current contract at Celtic is due to expire at the end of the season, and it is still unknown whether he will be offered a new deal.
The 40-year-old boss has not won over all the supporters at Parkhead, and there have been suggestions that they could look elsewhere.
The likes of David Moyes, Michael O’Neill and Neil Lennon are amongst the favourites to take over at Celtic, if Deila does leave.