Speaking for the first time about the incident at his weekly press conference on Friday, manager Mourinho said: "We feel ashamed, but maybe we shouldn't. I refuse to be connected with these people.
"I felt ashamed when I knew what happened. I am connected with Chelsea. I am connected with so many good things. I left Chelsea in 2007 and I could not wait for the moment to come back. It's not because of people like this that I came back.
"This is not Chelsea FC. But I repeat, I am a proud Chelsea club manager, because I know what this club is. These people don't represent the club. We apologise to the gentleman."
On Tuesday night, a group of Chelsea fans on their way to the Champions League tie with Paris Saint-Germain in the French capital refused to allow a black Frenchman to board a Metro train and were captured on video chanting racist slogans.
Chelsea have since suspended three people from attending matches at Stamford Bridge.
Mourinho also backed a campaign for the club to invite Souleymane S, the victim of Tuesday's racist abuse, and his family to London for the second leg of the European tie with PSG and a spokesperson confirmed chairman Bruce Buck had already written to Souleymane.
"He would watch not just the game, he would feel what Chelsea is," Mourinho said. "Because in this moment maybe he has the wrong idea of what Chelsea football club is.
"We would show Souleymane we are different.
"Chelsea is the owner, the board, the manager, the people who work here. They are the true people who support Chelsea.
"I do not know the gentleman, don't even know if he loves football, but for sure he would love to feel that the miserable people that had this action, are not Chelsea. I would support him coming."
Chelsea press officer Steve Atkins was directly asked about Abramovich's reaction and he replied: "He is disgusted. We have spoken to him and kept him abreast of what is going on. His reaction was that he is disgusted."
Before Mourinho faced any questions from the media, Atkins issued a club statement on behalf of the club and Abramovich. He said: "I would like to make it clear on behalf of everyone at the club our disgust at the incident on Tuesday.
"We were appalled by what we saw and the club would also like to apologise unreservedly to Soulemayne for the behaviour of the small number of individuals. We have operated fully and we will continue to do so.
"We have also conducted our own investigation and that is being shared with the police. We have suspended three individuals pending completion of investigations.
"It is only right that we complete our investigation to establish all facts. We have taken swift and decisive action. The people involved do not represent Chelsea FC, they do not stand for the values of this club and they have no place in the club ethos.
"This has been echoed by the vast majority of Chelsea supporters. We would like to thank the Chelsea fans who have come forward. We are proud of diversity here and the fight against discrimination."
When asked if the incident had affected his players, Mourinho, whose side face Burnley at home on Saturday, added: "We have 12-14 players with African connections and over the years this dressing room, I am sure this dressing room has always been a dressing room with big principles of equality.
"We have everything, not just about race, but religion and everything, so the dressing room reacted the same way: with disappointment, obviously condemning the situation and supporting the gentleman involved but always with the feeling that we are ashamed but maybe we should not be because we do not belong to these people.
"Since minute one after the incident, Chelsea has done everything because zero tolerance must be shown. Apart from that we still have to believe we are a great club and we have no space for these people."
The UN human rights office on Friday strongly condemned the racism of a group of Chelsea footbal fans toward a black French man on the Paris metro.
The commuter, identified as 33-year-old Souleymane S., was seen in amateur video footage being repeatedly pushed back off the train as he tried to board it on Tuesday with the fans chanting: "We're racist, we're racist, and that's the way we like it!"
UN human rights office spokesman Rupert Colville not only condemned the behaviour but said he hoped people would build on the outrage over it to fight racism in all its forms.
"We strongly condemn the racist behaviour of a group of Chelsea football fans during the build-up to a Champions League game in Paris on Tuesday," Colville told reporters in Geneva.
"The fans were filmed singing a song that flaunted their racism and repeatedly preventing a French citizen of African descent from boarding the Paris metro by shoving him back onto the platform," he said.
Colville recalled how his office has been involved in talks with football governing bodies FIFA and UEFA about how to "enhance the effort to drum racism out of football" after many racist incidents involving fans, especially inside stadiums.
Tuesday's incident in the Richelieu-Drouot Metro station in Paris showed "that much work remains to be done before racism is truly eradicated from the sport, let alone from society at large," Colville said.
"The fact that this particular incident was filmed and widely shown in the media has given rise to widespread and welcome condemnation by politicians, media and other commentators," he added.
"It is important to build on the outrage created by this snapshot of the ugly face of racism to re-energise the effort to combat it in all its forms wherever it occurs," Colville said.
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