Dujardin has been provisionally suspended by equestrian’s governing body the FEI.
Hester gave Dujardin a job at his yard in 2007 and has been a mentor to her during her career.
The pair won team dressage gold at London 2012, silver in Rio in 2016 and bronze in Tokyo three years ago.
Dujardin said the incident was “completely out of character”, adding: “[It] does not reflect how I train my horses or coach my pupils, however there is no excuse.
“I am deeply ashamed and should have set a better example in that moment.”
Asked about Dujardin, Hester said: “I haven’t seen her and I know things are very, very difficult but she’s surrounded by people who are trying to help her.
“She obviously accepts what she did, which she had to do and I am glad she has done that, for her.
“This is four years ago, people do make mistakes – what do we do, never forgive people for all the things that have happened?
“That is not my opinion of Charlotte. That video is fairly obvious and nobody is going to support that, you can’t, but my personal opinion of Charlotte over 17 years, I have not seen that, that is not her.”
Hester, Becky Moody and Charlotte Fry began their in the individual and team dressage bids on Tuesday.
Combinations perform a set test, with judges marking each of the movements out of 10.
The scores helped decide which 18 riders qualify for the individual final and the 10 in the teams final.
Moody, who replaced Dujardin, qualified for the individual final with a score of 74.938%.
Hester will have to wait for confirmation, having finished third in his group, but with a good score of 77.345%.