The incidents took place in the second leg of the second-qualifying-round clash at Celtic Park, with Neil Lennon's men progressing from the tie 5-0.
A statement issued on UEFA's website read: "Celtic FC have been fined €5,000 after a charge of improper conduct of supporters (setting off of fireworks) in their second qualifying match at home to Cliftonville FC on 23 July 2013."
The Scottish champions progressed through all the qualification rounds to reach the group stages.
After overcoming Cliftonville in the second round, Celtic sealed a narrow 1-0 aggregate win over Swedish side Malmo.
Shakhter Karagandy were dispatched in the play-off round 3-2, with James Forrest's 90th-minute goal sealing a memorable win at Celtic Park after a 2-0 first-leg defeat in Kazakhstan.
They will feature in Group H in the competition proper alongside Ajax, Milan and Barcelona.
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