The West Indies had needed 19 runs from the final six balls to secure an unlikely victory over England on Sunday as Stokes stepped up to bowl.
The English were stunned, however, as Carlos Brathwaite hit four consecutive sixes to wrap up a famous win in Kolkata.
"Watching it you are just gutted for him. It was almost written in the stars that Brathwaite was going to hit those four balls for six," Finn, who missed the tournament through injury, told Sky Sports News.
"I was sat on my sofa totally distraught for him and all the other guys out there because they have put in a great shift throughout the World Cup."
Stokes later admitted that he has been "overwhelmed" by support following the defeat.