Australia collapsed to 29-4 in the run-chase before Renshaw struck 65 off 44 while Glenn Maxwell scored 31 to get them back into the contest going into the death overs.
Both batters however lost their wickets at crucial stages as Australia folded to 146 all out and fell to a 23-run defeat in Colombo.
"We probably should have chased that down," Renshaw said after the game. "I don't think it's the bowling group that should get the blame today.
"(Zimbabwe) bowled really well at the start, took some early wickets, and felt like every time we built some momentum, they got a breakthrough.
"That partnership with Maxi was important. But we couldn't get enough momentum in there to chase that down. It was too many."
Australia have started the T20 World Cup without captain Mitch Marsh, who has missed the first two matches due to a groin injury.
Renshaw has still backed the squad to come to the fore despite missing their skipper at the top of the order.
"I think our batting group is so fluid with different options," Renshaw said. "With our experience in Big Bash cricket, we're very suited to going in different spots throughout the middle.
"Having Mitch out is a big loss and not sure when he'll be back. He's a big player to open the batting, and when he's not there, someone else has to open.
"So we have those differences in where people are going to be. But in terms of fluidity, I think we're all pretty able to manipulate and manoeuvre around different conditions. Unfortunately, we just lost wickets the wrong time."