"I thought we competed on the offensive side great all night," La Russa said. "I wish we could average six runs a game for the rest of the series."
The Cardinals, who scored a run in the first innings of their Game 4 and Game 5 victories over the Phillies in the NL Division Series, got out to an early lead yet again in the opening frame.
Jon Jay started it off with a one-out walk and reached second base on a single from Albert Pujols before scoring on a single from Matt Holliday.
The Brewers, however, struck right back with two runs in the bottom of the inning -- coming on a homer from Ryan Braun -- but the Cardinals countered with a key homer of their own in the fourth.
David Freese provided the big blast, jumping on a first-pitch curveball from Greinke that carried over the right-field fence for an opposite-field, three-run shot.
"Against good pitchers like that, you try not to waste any time looking for a pitch to hit," Freese said. "I'm the type of guy who goes after it. I got a pitch to hit, and I had enough backspin on it to get it out of here. It just kept going a little bit and crept over the wall."
Lance Berkman gave the Cardinals another run against Greinke in the fifth, as he provided a two-out single to score Rafael Furcal, who led off the inning with a double.
It appeared the Cardinals were headed to a Game 1 win with left-hander Jaime Garcia on the mound, but the Brewers roared back with six runs in a fifth inning that included two-run homers from Prince Fielder and Yuniesky Betancourt.
The Cardinals still battled and had a chance to tie it up with Pujols at the plate and runners at the corners and nobody out in the seventh, but Pujols grounded into a double play. A run scored, but the St. Louis threat ended there.
"I had a good pitch to hit, but I just missed it," Pujols said. "You throw me that pitch, I bet you seven out of 10 times I put that ball in the seats."
The loss was similar to their Game 1 loss to Philadelphia in the NLDS, as they had an early 3-0 lead but were done in by Philadelphia's five-run outburst in an 11-6 loss.
"The same thing happened to us in the first game against Philly, and we were able to regroup," Berkman said. "So we'll have to come back tomorrow ready to play."
Freese had a similar take on the loss, as the Cardinals have been defying the odds all year with their run to the postseason and their first-round win over the Phillies.
"I don't even think our backs are up against the wall," Freese said. "I think tomorrow will define where we're at in the series. We'll either go down 2-0 or go back home tied up. So if we win tomorrow, I'll take that."