Striker McBurnie stepped off the substitutes' bench in the 82nd minute to make his first senior appearance as a replacement for Nahki Wells and Parkinson insisted the 17-year-old had justified his inclusion.
"Ollie was on the bench because he had earned his chance," Parkinson said after his side's disappointing 3-0 defeat at New York Stadium.
"He wasn't there as a token gesture because it was the FA Cup.
"He was on there because he has scored goals for the youth team and because he has been outstanding in training.
"He has shown great enthusiasm when he has trained with the first team recently and he showed that again."
McBurnie, who signed a three-year deal with the club in August, has scored 17 goals in 10 appearances for the youth team this season and has been selected to take part in a two-day training camp this week with the Scotland Under-18s squad.
- Sports & Recreation
- Nahki Wells