The 39-24 win was Glasgow's first over the defending champions in Dublin since 2011.
It moved Warriors back ahead of Munster at the top of PRO14 Conference A, and a win against Edinburgh next will secure a home semi-final.
"This time last year we limped into the play-offs - we had a massive lead," Rennie told BBC Scotland.
"I wasn't that upset seeing Munster get home (by beating Benetton) Friday night because it kept the pressure on us. I think it brought the best out in us.
"We're aware of what it's going to take to win a title. So we've got three big games left hopefully."
They were they were forced to make 307 tackles against Leinster, and Rennie was pleased with his side's resilience.
"We were pretty embarrassed by the Saracens performance, especially defensively," the New Zealander said. "So a couple of big Irish sides who carry hard has been a good test for us, and it's about attitude."
Edinburgh on April 27 are all that stand in Glasgow's way in their bid to secure a home-semi final, but Richard Cockerill's men have already got the better of them twice this season.
"They're the type of team that can choke you," said Rennie. "They don't play an enormous amount of footy but they defend very well and they've got a good kicking game. We know what's coming."
Securing a home semi could result in the Warriors having Nick Grigg and DTH van der Merwe available for the play-off run. Ryan Wilson is targeting a comeback in the Edinburgh game and Callum Gibbins will be available for that fixture as well.