McBurnie, who scored 21 goals for the club's youth team during the first part of this season, made his second senior start at the weekend in City's home draw with Bristol City.
The appearance was his sixth in total for the club after making his debut as a late substitute during the F.A Cup tie at Rotherham United back in November.
The 17 year-old talent collected 77 minutes under his belt in the Bristol City match and twice came close to netting his maiden Football League goal during the second period.
Parkinson was pleased with the forward's efforts against Bristol City but stressed that it is important that he isn't given too much of a workload too early.
The City chief said: "It was a tough game because they (Bristol City) came with three centre backs in their side and big Marvin Elliott just ahead of them, but I thought he did well.
"He worked his socks off.
"He nearly got his goal as well but we know he is going to be a good player for us.
"We just have to make sure that we expose him to first team football at the right time. We have to give him the right amount of football for him at his age.
"We have a good player there in Ollie but we want to treat him well and make sure that our supporters will be able to enjoy watching him for many years to come."
After joining the now-departed Nahki Wells in attack for his first senior start against Rotherham on Boxing Day, McBurnie was paired up front this time with James Hanson for the Bristol City fixture.
Parkinson felt McBurnie's strike-partner at the weekend also deserved some praise for the level of his performance.
He added: "You have to give a special mention to James as well.
"He put in a real 'number nine's' performance. He held the ball up well and got his goal.
"That's his seventh goal of the season now - all from open play as well. That's not a bad effort at all from a striker who is playing at this level for the first time."