Birmingham midfielder Dunn, 27, passed a Bolton medical and was discussing personal terms before Blackburn tabled a late £2.2m bid for him.
"He's told me that's where he wants to go - simple as that," said Allardyce.
"At the 11th-hour they have pinched him. We are extremely disappointed, but there is not a lot we can do about it."
Allardyce added: "I always feel let down when you have got so far down the road spending so much time showing the player this is the best place to be to get his career back on track.