Both sides had openings in the early stages and it was Forest who broke the deadlock in the 20th minute.
Forest had the chance to double their lead from the penalty spot a quarter of an hour later, but Henri Lansbury fluffed his lines and Forest were immediately punished as Kenneth Zohore tucked home a penalty for Odense.
The heavens opened at the start of the second half and Forest handled the conditions better early on after the interval.
However, it was the Danish side who scored the third and then quickly added a fourth to go two goals in front as Rasmus Festersen and Zohore found the net.
The Championship season is exactly a month away and Dougie Freedman's side next face Mjallby on Sunday.