The former Arsenal and England striker flew home from Brazil after learning that a group of men had broken into his home on Wednesday night, taking cash and valuables, including the 50-year-old's MBE medal.
After arriving back in the UK, Wright told The Sun: "They threatened to cut her fingers off and even threatened to do the same to the children, who were both upstairs in their bedrooms.
"Nancy was praying the children wouldn't wake up. It would have been devastating for them to see what was happening.
"All I want to say really is me and my missus, my girls, everyone's safe. The police are trying to get on with what they are doing. What's really disappointing is they're from an age group I've worked with and tried to help."
Among the items taken were several watches, including an Arsenal one with an inscription from the club, and another that was a gift from former teammate Dennis Bergkamp.