The 26-year-old left the Scottish Premiership side last month after making a £350,000 switch to Uzbekistan outfit Pakhtakor Tashkent.
Goncalves has now told the Edinburgh Evening News that racist abuse directed at him from "a minority" of Jambos supporters and heard by his family had been a major factor in his departure.
"In relation to the recent report of racial abuse directed towards Isma Goncalves, Heart of Midlothian Football Club wishes to make it very clear that it abhors racism and any type of prejudicial abuse, and will not tolerate any incidence of such behaviour," Hearts said in a statement.
"The club is committed to providing support for its players and a safe working environment for all staff, and if anyone is proven to have made racial remarks to individuals inside the stadium then they will be subject to an immediate football banning order and we will report every single such incident to Police Scotland for action.
"We would urge supporters who witness any such behaviour to contact the club, be it in person at Tynecastle, via our Supporter Services email address, by phoning us or by texting our incident report line in confidence, which can be found inside the stadium's concourse.
"We are aware that, as ever, it is only a very small number of individuals who have let the club and themselves down in this manner.
"The club was unaware that these incidents had occurred, but we will immediately implement some additional proactive measures to ensure there is a simple and easy process for players and their families to report any such incident.
"We pride ourselves in being a multi-race and multi-cultural club and will take all steps to ensure that players and their families who join us here in Edinburgh, can do so, free from any concerns over prejudice.
"The club will be contacting Isma to apologise to him and his family on behalf of the thousands of supporters who share our anger and disappointment that they were subjected to this behaviour."
Goncalves scored 15 goals in 42 appearances for the Edinburgh-based club.