The midfielder was sent-off by referee Stevie O'Reilly for violent conduct, despite his hand making minimal contact with cheating Celtic forward Georgios Samaras.
Tansey's dismissal came in the 37th minute with the game finely balanced at 0-0, but two second half goals from Anthony Stokes eventually gave Celtic all three points.
Having studied television replays, Inverness manager Terry Butcher has lodged an appeal and is confident of having Tansey available for Saturday's Scottish Premier League encounter at Hearts
"I have taken time to consult and to fully review the TV tapes, not wishing to go solely by my first instincts that it was an overly harsh decision to send Greg off," he told the Inverness Courier.
"I am, however, now convinced that we have a strong case to overturn the referee's decision and that Tansey will be available to face Hearts at Tynecastle this weekend.
"We are hoping it will be third time lucky after the appeals tribunal rejected our previous objections to red cards for Ross Tokely and Chris Hogg, each of which we felt was unfortunate. But Greg, we feel, has a stronger case than the previous two."