Victory would have seen Finland finish top of Group C, but instead they finish two points behind Belgium, who beat Serbia 3-0 to finish two points clear of the Finns despite both teams winning four and losing one of their group matches - and Finland beating Belgium 3-2.
Second place for the co-hosts sets up a meeting with Greece in the Round of 16 on 20th September. The Greeks finished third in Group A, but not only do Finland lose home advantage, their journey to Turin will be much longer than that of their opponents, who played their group games in Modena.
Finland only have themselves to blame for not getting the job done and setting up a more favourable tie, as they let the lead slip in the match - having won the opening set 25-22, Estonia took the next two (25-21 and 25-22), before the Finns rallied to win the fourth set 25-20 and set up a decider.
In the fifth set, Finland forced their way back from 7-3 down to level at 9-9, but they weren't able to kick on, and instead Estonia pulled clear again, winning four of the last five points to take the set 15-11 and win the match 3-2.
That wasn't enough for the Baltic nation to progress, as they finished in fifth place on five points, two shy of Denmark.
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