Peter Casey has insisted if anyone voted for him because they thought he was a racist and against Travellers, they voted for the wrong person.
Controversy surrounded the candidacy of Mr Casey who criticised the community as part of his bid for the Aras last year.
The former presidential candidate said he never had a bad experience with a Traveller.
Mr Casey said: "If the 342,727 people who voted for me, if they voted for me because they thought I was a racist, if they voted for me because they thought I was against Travellers, then they voted for the wrong person and they should change their vote.
"I have never had a bad experience with a Traveller, ever. There is a very small percentage of Travellers that are giving the Travellers a bad name."
However, a co-ordinator with a Dublin Traveller support group has said she got "derogatory mail" for the first time in the wake of the Presidential campaign.
Angela O'Neill from the Finglas Traveller Development Group told Mr Casey that she was astounded by the mail she received.
She said: "The day of the vote I received an email that I was astounded by. Somebody had gone to great trouble to set up an email address under the name of 'MichaelthePikey' and it was agreeing that Irish society is sick of this lot who are basically a non-taxing, scrounging, anti-social shower.
"And on the morning of the count from the RDS, I received another email saying '21%. What do you think of that? ha ha ha'."
As Mr Casey visited the Dunsink site in Finglas, one resident told him of the discrimination he faced at school at a young age.
The businessman condemned those who would verbally abuse travellers attending school.
He said: "Absolutely totally wrong and it shouldn't happen. I condemn anybody that does that behaviour and I'd be very surprised if that behaviour exists today."