He said: "I honestly still do not quite understand what happened.
"I went to Scotland but didn't do any medicals nor participate in training sessions.
"Throughout the three days, all I had to do was wait until they bought me a ticket to return home. I was given no explanations by any of their managers.
"Naturally, I would like to test myself playing for such a famous team."
Celtic refuted the player's claims, saying he was treated with "the utmost respect".
Despite the experience, Verkhovtsov's agent hopes a move could be resurrected at the end of the season.
Valeri Isayev said in the Scottish Sun: "Initially, we talked not about a full-scale contract but a half-year loan.
"Celtic let us know their conditions, but when we arrived in Glasgow those were changed.
"As a result, we failed to reach agreement. I don't want to go into more details about it now.
"As for Verkhovtsov's transfer value, it was not even discussed.
"We are going to return to the issue in summer."
Meanwhile, Celtic are trying to finalise a deal for Derry teenager Darren McCauley, according to the Irish club's manager.
The Hoops have reportedly beaten off interest from Blackburn in the 18-year-old midfielder.
Derry boss Stephen Kenny said in the Daily Express: "Celtic are talking to Derry at the moment to try to thrash out a deal.
"There is a lot of interest in Darren but it looks like he will be going to Celtic."