Having been level at the interval, three second-half tries gave the Warriors a bonus-point and a 31-10 victory over Ospreys.
Speaking to glasgowwarriors.org, Rennie said: "We're happy to get the five points today against a good Ospreys side.
"I thought they had the better of us in the first-half, but going in at 10-10 we felt like they'd fired a lot of shots, whereas we hadn't yet.
"We raised the tempo and built some pressure in the second half, which was pleasing. I'm happy with the end result, but from a coaching point of view I know we can do a lot better. It'll give us an edge in training this week as we prepare for Cardiff."
A capacity crowd of 7,351 were in attendance for Rennie's competitive home debut, and the former Chiefs head coach was quick to underline his appreciation for the support of the supporters.
"I loved it," said Rennie.
"The crowd were really vocal and it was nice that we gave them something to sing about.
"I know we can play better than that though, so the guys will continue to work hard."
Glasgow travel to Cardiff next weekend and Rennie expects his players to raise the intensity in training this week.
He added: "Cardiff Blues have had a couple of losses, so that'll probably have made them tougher. They'll probably bring a couple of guys back that have been on rest until now, too.
"We'll have to much better than we were today, both with and without the ball."