Manager Gordon Strachan wanted the 34-year-old Dutchman to fill the boots of the recently-departed Welsh striker and was in Amsterdam on Monday to discuss a move to Parkhead with the player.
But, despite the player’s willingness to drop his wage demands, the club still could not do a deal.
The summer exits of Hartson and Roy Keane have left the Hoops short of experience and Hasselbaink’s agent Humphry Nijman believes he would have been a major asset for them.
“It is possible they have missed out,” he said. “We got down to a level which was the best we could do but unfortunately that was not enough to do an agreement.
“Jimmy is very sad because he would have loved to have played for them and Gordon really wanted him there.
“It’s known that a lot of young players have come to Celtic and the squad is reasonably young.
“Gordon wanted to add some experience to that group and Jimmy was the perfect man to help those around him – not only on the pitch but also in the dressing room.
“But you have to understand that if a club cannot reach an agreement then we have to respect them, just like clubs have to respect a player when he decides where he wants to play. We have three Premiership clubs interested in him and we will be speaking to them now.”
Celtic also verified earlier reports a deal could not be sealed and both parties parted amicably.
Chief executive Peter Lawwell said: “We tried all we could to sign Jimmy but unfortunately it wasn’t to be. We wish him all the best.”
Meanwhile, Alan Thompson fears Celtic’s gruelling world tour could jeopardise their hopes of silverware this season.
The midfielder spoke as the players moved from Warsaw to Krakow on the latest leg of a marathon tour which takes them to the US next week then Japan between the first and second games of the new Bank of Scotland Premier League season.
Gordon Strachan’s team also have friendlies at home against Everton and Manchester United and a trip to Chelsea.
“I don’t know what input, if any, the manager had when the schedule was put together but it does seem particularly long. Going to Japan isn’t ideal and our complete programme seems too much.”