The club's Supporters' Trust strongly criticised Ze Zerbi appointment after he defended Greenwood when he signed for French side Marseille when the 46-year-old was their coach.
Speaking to Spurs' club website, the Italian said he was "sorry if I offended anyoneâs feelings with this subject matter".
Giving his response in Italian to avoid any confusion over his statement, he said: "I have never wanted to downplay the issue of violence against women or violence against anyone more broadly.
"I hope that over time people will get to know me better and will understand that, at that moment, I didnât mean to take a stance".
He added: "In my life Iâve always stood up for those who are more vulnerable, more fragile. Iâve consistently fought and taken a stand to be on the side of those who are most at risk.
"Those of you who know me well will know that Iâm not the kind of person who makes compromises to win more games or to win an extra title".
Former Manchester United striker Greenwood was charged in 2022 with attempted rape, controlling and coercive behaviour and assault occasioning actual bodily harm.
However, the Crown Prosecution Service dropped the case in February 2023 following a combination of the withdrawal of key witnesses and "new material that came to light."
Greenwood, 24, denied all allegations against him and De Zerbi appeared to take the stance that because he had not been found guilty he deserved to be allowed to continue to pursue his career while the pair worked together at Marseille.
The Tottenham Hotspur Supportersâ Trust opposed the appointment which was announced on Tuesday, expressing "serious and far-reaching concerns" over his past support for Greenwood.
The Trust said his arrival placed a "heavy strain" on unity at a time when Spurs are battling against relegation from the Premier League.
It also demanded that the football club and De Zerbi publicly reassert their "commitment to the values that fans hold dear â chief among them equality, respect, and integrity".
A statement read: "While we recognise the limited pool of managers with recent Premier League experience, and the need to act with urgency as Spurs face the prospect of relegation, this appointment raises serious and far-reaching concerns, and many fans have been in touch with us to urge us to communicate the strength of feeling.
"De Zerbiâs comments about Mason Greenwood were unnecessary, ill-judged, and deeply offensive to a significant number of supporters and, without doubt, will have left victims of male violence alarmed.