Replacing the injured Ricky Ravenhill after only 22 minutes, Kennedy came into the action and produced a hard-working performance in central midfield alongside skipper Gary Jones.
For Kennedy, the appearance against Steve Cotterill's Robins at the Coral Windows Stadium was only his seventh of the season so far in the league following stern competition for a midfield slot with the likes of Jones, Ravenhill and Nathan Doyle.
Parkinson was pleased to see the summer signing come on at the weekend and make an impact, and he hopes the former Rochdale man can now show supporters more of what he is all about in the future.
Parkinson said: "Ricky (Ravenhill) started the game fantastically well and it can sometimes be hard for someone to come into the middle of a match and replace a player who has been playing well.
"I thought JK (Jason Kennedy) did well though.
"I am desperate for Jason to do well. He played and scored for us at MK Dons (back in November) and then I took him off at half time in the next game against Notts County.
"I knew it was the right decision for the game at that time but it can have a detrimental effect on the player in terms of their confidence going forward.
"Jason is a player who has played at this level for Rochdale, won countless Player of the Year awards for them, and we have faith in his ability.
"Like with all of the players we bring in, we need the supporters to stay right behind him and give him every chance.
"As he showed on Saturday, he's a good player."
Another player taking the opportunity to shine on Saturday was Carl McHugh.
The hard-working Irishman was brought back into the side at left back following James Meredith's training ground injury last week.
And despite the position not being the defender's most natural, Parkinson felt McHugh didn't let anyone down with his wholehearted performance.
Parkinson added: "If you ask Carlo, he'd probably say that he is most comfortable left-side centre back. But he was great and he was never going to let us down with his heart and his commitment.
"He never gives in, he has great spirit, and he typifies what we are all about."