"Not being able to clinch Roy's signing is particularly disappointing because that is a world-class player you are talking about," said Bolton boss Allardyce.
"From my point of view it was a top-class player, who, on 1 January, I could put into the team and say 'this man is going to make us better'.
"I had no doubts at all about that. Where I can go and find that now is virtually impossible."
"We were right there as one of the two or three clubs he was going to choose from," added Allardyce. "When you come so close - but yet so far - it is an even bigger disappointment than just a straightforward 'no'.
"Yet I am pleased we got to the stage we did, the way the negotiations went and by the fact it does not appear to the financial side of it where Roy has made the choice.
"It's down to his childhood dream of playing for Celtic and to the size and pull of that football club.
"We would like to wish him all the very best."