After in-form winger Andros Townsend gave Tottenham a first-half lead a flare was thrown from among the celebrating visiting supporters, which struck Bryan on his back.
West Midlands police were aided by Tottenham supporters in the Doug Ellis stand to identify the perpetrators and swiftly arrested a 25-year-old and a 47-year-old man.
And Villas-Boas hopes this will be an isolated incident.
“It is not great to see, it should be avoided completely,” he said.
“It touched the linesman and situations like this don’t have a place in football.
“I sincerely hope it doesn’t happen again.”
Spurs could yet face further punishment, with the Football Association set to conduct it’s own investigation into the incident.
“The FA will investigate this matter, which is unacceptable,” said a spokesman.
“We will await the match officials’ report and will be speaking to the clubs.
“Such incidents highlight the dangers of pyrotechnics being used in a football stadium.”