Leigh Griffiths grabbed his 40th goal of the season - the first Celtic player to reach the 40-goal mark since Henrik Larsson in 2004 - but finished up on the losing side as Ulsterman Tommy Wright's St Johnstone came from behind to win 2-1 at McDiarmid Park.
After a goalless first-half, the Scotland striker opened the scoring eight minutes after the break, but the champions then contributed significantly to their own downfall.
Just two minutes later, Saints striker Steven MacLean robbedStefan Johansen outside the box to level before a mix-up between defender Efe Ambrose and stand-in goalkeeper Logan Bailly in defending a cross in the 77th minute allowed sub Graham Cummins to shoot into an empty net to ultimately clinch their fourth-placed finish.
Griffiths became only the eighth Celtic player in history to reach the 40-goal mark but is suspended for the last game of the season at home to Motherwell on Sunday, where departing Ronny Deila will look for his side to tighten up before he leaves for pastures new.
Griffiths said: "I'm pleased to have scored but the main thing is the team and we're disappointed not to win.
"To get mentioned in the same breath as players like Larsson is something I've got to cherish.
"I've got another five years and if I can keep this form for the next five I'll be happy."
Saints, as they should, will celebrate their fourth post-split victory.
The home side applauded the champions on to the pitch then set about preventing them getting into any sort of rhythm.
But after a first-half of few chances, there was plenty of excitement in the 53rd minute when Johansen played in Griffiths and he eased past Tom Scobbie and Joe Shaughnessy before knocking it past Clark, then racing behind the goal to celebrate with the travelling fans.
However, two minutes later the home side drew level with a gifted goal when dithering Johansen was caught in possession by MacLean, who went through to cleverly chip Bailly for his 15th goal of the season.
And Celtic had not finished with mistakes.
Shaughnessy's cross from the right saw Ambrose and Bailly collide with Cummins, on for MacLean, gleefully knocking the ball into the empty net.
St Johnstone: Clark, Shaughnessy, Anderson, Scobbie, B Easton, Wotherspoon, Brown, Craig, Swanson (Doyle 90), MacLean, Kane (Cummins 59)
Subs: Mannus, Sutton, Hurst, McCawl, Krachunov
Goals: MacLean (56), Cummins (77)
Celtic: Bailly, Janko (Ralston 74), Ambrose, Sviatchenko, Izaguirre, Johansen (Bitton 66), McGregor, Roberts, Allan (Rogic 80), Christie, Griffiths
Goal: Griffiths (53)
Subs: Armstrong, Fasan, Forrest, Tierney
Referee: Willie Collum