The former Hoops midfielder says the club have not rebuilt and have failed to ensure the gap between themselves and Rangers remains wide.
Former Celtic midfielder Stiliyan Petrov has told the Scottish Sun that he is disappointed and worried that his old club have not widened or even maintained the gap between themselves and arch-rivals Rangers this season.
The Hoops look set to win a fifth Scottish Premiership title in a row this season, but have been far from convincing on occasions throughout the campaign.
Meanwhile, Mark Warburton has led the Gers to the Scottish Championship title and the Petrofac cup, and his side will return to the top flight to challenge the Bhoys next term after a four-year absence.
Most concerning for Celtic was the way in which they lost to their arch-rivals on penalties in the Scottish Cup semi-final at Hampden Park on Sunday.
Rangers looked the better side for the majority of the match, twice taking the lead against Ronny Deila's side, and Petrov says the lack of any obvious gap in quality between the two clubs is cause for real concern ahead of next season.
The Bulgarian, who scored 62 goals in 312 appearances in seven seasons at Parkhead, told the Scottish Sun: "I thought with Rangers not being in the top league Celtic would have done their best to make sure the gap would be even bigger when they came back. But watching the game on Sunday, I couldn’t see that gap. That was the most frustrating thing.
"Have they spent well? Very doubtful. Have they built? I’m not sure about that. And are they further ahead of Rangers? Well, watching Sunday, I don’t think so, and that is worrying. With Rangers coming into the top league, they will push Celtic. Even with the team they have at the moment they showed more passion and hunger for success.
"I’m sure they are going to build a team that is going to push Celtic next year. It’s going to be tougher for Celtic because they haven’t rebuilt. Celtic may have to spend more than Rangers in the summer. They have to bring in more quality because Rangers will really fancy their chances."
Ensuring that they remain Scottish football's dominant side will be the main remit of whoever is appointed as Ronny Deila's replacement this summer, after the Norwegian announced earlier this week he would be stepping down at the end of the season.