The Italy international was confronted last month.
Udogie, speaking about the incident for the first time, told The Athletic: “The club showed me good support and was next to me every day.
“I’m really grateful to them for what they have done and for keeping me and my family safe. It’s really good for me.
“Obviously, it was important (to feel that support). Because it’s a new city for me. It’s my third year (at Spurs) but obviously London is a big city.
“So to be here with my family and my daughter, it’s good to have the club around me.”
Asked if he was shaken by the incident, Udogie added: “Yeah, of course. It was not something I’d wish on anyone.
“It was a shock. But it’s OK, now we look forward.”
The Sun reports a 31-year-old man who works as a football agent was arrested on suspicion of making threats with a firearm and remains on police bail.