Burke, who was replaced by Nathan Clarke at the interval on Tuesday evening, is likely to be sidelined for only a short period after scans thankfully revealed just a slight issue with his Achilles.
Parkinson said: "There was some initial concern over Reece because he was getting some pain down the back of his heel every time he put his foot down. But we've had it scanned and it is just a minor strain to one of his ligaments.
"That is obviously good news for Reece and for us, and hopefully it won't be too long out for him.
"With Billy Clarke (hamstring injury), he will probably be out for two-to-three weeks.
"It is shame for Billy but that is sometimes what happens when you play on heavy grounds at this time of year. It also gives someone else a chance to stake a claim in the team."
Lee Evans will serve the second game of a three-match ban this Saturday, while Jamie Proctor is ineligible to play against parent club Fleetwood as part of his loan deal from the Cod Army.