Warriors let a seven-point lead slip against an Edinburgh side reduced to 14 men for 74 minutes after prop Simon Berghan was red-carded for stamping.
Rennie, who watched his side squander numerous scoring opportunities, believes the first PRO14 defeat of the campaign should prove a turning point as Warriors indiscipline and high error count cost them dear.
On the defeat, he said: "We were embarrassed. That's nothing against Edinburgh, they are a good side in good form but up 7-0 against 14 men for 70 minutes and had so many opportunities to put them away and didn't.
"We just have to be a hell of a lot better and a hell of a lot more urgent this week.
"Hopefully, we look back on this as a bit of a turning point but we have been talking for a number of weeks."
He added: "We lost both times to Montpellier when we had done more than enough to win but errors and discipline hurt us.
"Obviously, we stumbled again at the weekend and if we have aspirations of winning a title we can't do that against good sides.
"Hopefully, we see a more clinical performance this week."