The Warriors scored six tries to earn their eighth bonus-point of the season, and now lead Conference A by 17 points.
But Rennie was unhappy with how his side dealt with Cardiff being reduced to 14 men after prop Taufa'ao Filise was sent off for a high tackle.
Speaking to BBC Scotland, a Rennie said: "It was a fairly grumpy coaching group to be honest. It was just the attacking balance - we over-did the pick-and-go, especially when they were down to 13 [when Olly Robinson was sin-binned].
"They had everyone around the ball, we just had to go left or right, but we were still trying to go through the middle of them.
"The red card changed things for both sides. I think we almost felt the game was over and we didn't have to work quite as hard. They are a very tenacious side and made us work for it.
"Some of the decision-making and execution wasn't good enough, but at times you have got to find a way to win ugly and we did that tonight.
"It would have been nice to have a bit more clinical performance, but I am happy to get the five points."
Rennie was pleased the likes of scrum-half Henry Pyrgos "got some serious game time under his belt" after being a replacement in his two previous Glasgow outings and all three of Scotland's autumn Tests.
Glasgow next face a European double-header against Montpellier, guided by former Scotland coach Vern Cotter, in the Champions Cup, with the French side coming to Scotstoun next Friday, 8 December.
Despite gleaning no points from their first two pool games, making qualification highly unlikely, Rennie says the Warriors "will have a crack".
"Strangers things have happened," he said. "We will put out a good side and we will have a crack. Based on what happens next week will determine what we do the following week in Montpellier.
"If we could win our last four games [in the group], we are in with a sniff, but it is a really tough competition.
"Unfortunately we didn't play well enough in the first two games. But four or five points next week and who knows? We will be having a crack."
The side to face Montpellier is unlikely to include full-back Stuart Hogg, who is still awaiting a definitive prognosis on a hip injury sustained in the warm-up before Scotland's final Test with Australia.
"He is due for a scan, so we will know the severity after that, and then find out what sort of time-frame it is," Rennie added.
"We are pretty confident he won't be fronting (playing) this week."