McGuinness, who missed the weekend’s Championship opening defeat to Sunderland with a minor hamstring injury, was part of a young Bluebirds side which saw off the Rovers challenge.
Bulut admitted McGuinness’ intervention had been key to the win, which was sealed by Welsh international Rubin Colwill’s injury-time effort.
The Cardiff manager said: “We needed just a goal to open up the game. This we did from the corner, a great header from McGuinness. It was a good goal.
“For us the game was then much, much easier because the opponent has to create, so we had enough space to try to score the second, even a third or a fourth.
“But in the end it was 2-0, we continue in the Cup, so that is good.”
Former Celtic midfielder David Turnbull had to be replaced in the starting line-up after sustaining a hamstring problem in the warm-up before the Rovers game. Eli King took his place.
Bulut hopes Turnbull’s injury will not be a long-term problem
“I hope it is not something serious. Tomorrow I hope we have better news.”
Cardiff are also monitoring the fitness of striker Callum Robinson, who sustained an Achilles problem against Sunderland and is due to have a scan.