The 26-year-old, who moved to Uzbek club Pakhtakor Tashkent in January, claimed that racially-motivated taunts "from a minority" of Jambos fans proved a factor in his exit.
Hearts announced on Wednesday that they will contact Goncalves to issue an apology, and Levein has now stated that he plans to do the same.
"I was obviously sad and slightly embarrassed that Isma didn't feel he could come to me and talk about it," Levein told BBC Sport. "That's on me and it's something I need to look at.
"If we have a player who has been struggling and has suffered racial abuse, then I need to make it easier for him to come and speak to me and talk about it.
"If you read the statement [from Hearts on Wednesday] you can see how clear [chairwoman] Anne [Budge] has been about this and how everybody is disgusted by what has happened.
"I have been trying to get hold of Isma and we're going to speak this afternoon and I will apologise to him about what has happened."
Goncalves, who was born in Guinea-Bissau but played youth football for Portugal, was in his second stint in Scottish football having had a loan spell with St Mirren from Rio Ave in 2013.