Angeleri, 27, was due back on Wearside on Wednesday on his return from international duty, during which he made his comments.
The Argentinian told ESPN Radio: "The boss doesn't talk to me, he doesn't even say hello to me when he sees me. I think he doesn't like me because I'm not English."
The same quotes were used in a report which recalled Aston Villa's French boss Gerard Houllier's remarks about Bruce's attitude towards him in the wake of Darren Bent's controversial £24 million move to the midlands in January.
However, the former Manchester United captain has hit back and pointed to the fact that he has 11 overseas players from nine different countries among his first-team squad of 25 as evidence to refute the charge.
Bruce, who said he is considering legal action, told the Sunderland Echo: "I'm deeply upset. In today's world, there is nothing more damaging than someone suggesting you are a racist.
"Of all things that have been thrown at me over the years, that is the charge that hurts the most. I have got no problem with criticism - I learned a long, long time ago that it's part and parcel of the job, and I never take it personally.
"I have always tried to look further afield for players, more so than the vast majority of managers - at Wigan I brought in a lot of South Americans; here I have brought in South Americans and Africans. It's ridiculous to accuse me of being racist.''
Bruce admitted he could even understand why Angeleri, who arrived at the Stadium of Light in a £2 million switch from Estudiantes in July last year, is so upset.
"I have left out a player who I paid a lot of money for and he has had his say," Bruce said. "I'm not too upset if a player has a pop because he's not getting in the team because if I was in that position, I would feel the same way.
"I try to treat him with respect, but I'm not picking him, so of course I can understand his frustration. There is a line you should not cross, though. I will deal with Marcos when he returns, and it will be kept in-house.''