Warriors looked eager to keep ball in hand but high winds and driving rain raised the error count. When Glasgow did take the kicking option they drew mistakes from Connacht and gained good field position.
"We wanted to be positive but we didn't kick enough, especially second half," head coach Rennie told BBC Scotland.
"We had some opportunities to sneak some ball in behind them and we tried to play in conditions that made it difficult.
"We probably needed to get better balance in our attack, but in the end we scored a couple of important tries, and one of them off a kick, so maybe a few more kicks would have been better options for us."
Glasgow outscored Connacht by two tries to nil, with both second-half touchdowns demonstrating sharp attacking play.
Substitute and debutant Adam Hastings combined with Peter Horne to put Ali Price in for the first, and scrum-half then turned provider with his cross-kick taken by Leonardo Sarto, who popped the ball up for fellow wing Lee Jones to go in at the corner.
"I thought our defensive line-out, our scrum and then our defensive line speed put them under a lot of pressure and ultimately we got rewarded by that," Rennie said.
"The players will have learned a lot from playing in those conditions. If we have to play in them again we'll be better for it.
"It confirmed what I knew - there's a lot of character in this group. We've got a lot of players to come back over the coming weeks, so that's exciting.
"A big chunk of these boys we'll need during the autumn and Six Nations breaks. I think technically we can get a lot better and tactically we can be a lot smarter, but attitude and everything, it's a crucial place to start from."
Adam Ashe made more carries (19) and tackles (21, missing one) than any other player and Rennie is confident good things lie ahead for the back-row man.
"He captained our side in the two pre-season matches; I think he's got a massive amount of potential," the New Zealander said.
"He's a really good athlete. He was prepared to carry the ball and created a lot of go-forward for us tonight, then got through a hell of a lot defensively."
The midweek signing of Nikola Matawalu took Rennie's tally of summer recruits to 12, and the 53-year-old does not expect to make any further additions to his squad.
"We're pretty much done," Rennie said. "We've got some guys to come back - Huw Jones when he finishes in South Africa will probably play for Scotland [in the autumn internationals] so we probably wont see him until December.
"Siua Halanukonuka is still to come in, but aside from that everyone is in the country. Callum Gibbins has had a couple of weeks to train, but we decided to leave him out tonight and back young Matt Smith who has been training for the last 10 weeks."
Hastings, a summer arrival from Bath, was stretchered off early in the second half with a gash on his leg, and taken to hospital for treatment. The stand-off had replaced Sam Johnson, who suffered an early head injury.
Wing Tommy Seymour was granted an extended break after touring New Zealand with the British and Irish Lions this summer, and should be ready to feature in the third or fourth round of league matches.