Suppan took a five-hitter into the ninth inning as St. Louis spoiled Sheets' record payday with a 3-0 victory over the Milwaukee Brewers on Friday night.
"They were both very sharp; there was nothing there for hitters tonight," La Russa said. "In this league, you face pitching like that."
Sheets, a two-time All-Star, signed a $38.5 million, four-year contract with the Brewers before the game, the richest deal in team history.
Albert Pujols hit his second home run of the season, a solo shot in the fourth. It was the second homer allowed by Sheets (1-1) this season.
Sheets went 7 1/3 innings, allowing three runs, two earned, and five hits. He struck out seven and walked one and downplayed any effect the contract might have had.
"It didn't impact me," he said. "I went out there and pitched. Pujols put a good swing on the ball, and I put some bad plays on the ball."
Suppan (1-1) made no such mistakes and finished just two outs from his first complete game and shutout since July 28, 2003, when he beat the Cardinals while he was with Pittsburgh.
Milwaukee had been swinging the bat very well since the season started. However, Suppan, who won a career-high 16 games in 2004, stopped them.
"I was able to keep them on the ground for the most part and let the defense do the rest," he said. "I was able to get some first-pitch outs, and that definitely builds on itself."
Suppan allowed only two hits after the third, both to Brady Clark, and struck out three and walked two in 8 1/3 innings. The Brewers never got a runner past second and the Cardinals turned two double plays to support Suppan.
"He was an artist," La Russa said of his right-hander's 102-pitch, 64-strike performance. "He did very, very well, obviously. It's about missing the middle of the plate, getting on the edges, changing speeds."
Suppan earned his third straight victory at Miller Park. He came in with a 7-2 career record in 11 appearances against the Brewers.
Jason Isringhausen got the final two outs for his third save of the season.
Sheets had signed a one-year, $6 million contract with the team in February to avoid salary arbitration but left open the option of a longer pact.
He had back surgery in the offseason, and general manager Doug Melvin wanted to see how the right-hander performed in spring training before opening talks on a bigger deal.
Sheets entered the game 4-8 with a 4.41 ERA in 15 career starts against the Cardinals, after going 1-3 in five starts against them last year.
On Friday night, Sheets started like he might have better luck against the defending NL champions.
The game turned around on Sheets in the fifth when he made two throwing errors that cost him.
"It turned out to open the inning for us," La Russa said.
Reggie Sanders reached on Sheets' two-base throwing error leading off the inning. Sheets seemed to launch the ball more than throw it to first.
Mark Grudzielanek followed with a run-scoring single. One out later, Suppan dropped a perfect bunt down the first base line that Sheets grabbed, but he threw the ball away. Grudzielanek, running on the play, scored easily to make it 3-0.
"That was uncharacteristic of Benny," Brewers manager Ned Yost said of Sheets, who has only made seven errors in his career. "He's normally a pretty good fielder. Those balls just got away from him."
The Brewers have not given Sheets any run support in his last two outings after providing nine in his Opening Day start in Pittsburgh.
Cardinals center fielder Jim Edmonds came down with a stomach flu and was scratched from the starting lineup. Right fielder Walker moved to center and Roger Cedeno started in right. ... The Cardinals placed right-hander Cal Eldred on the 15-day DL with a viral infection, retroactive to April 11, and recalled right-hander Jimmy Journell from Triple-A Memphis.