But Greinke, who signed a six-year, $206.5 million free-agent deal this winter, holds himself to a higher standard than that.
"Overall it wasn't very good and needs to be better," Greinke said. "I'll do what I can to do better from here on out. Just too many mistakes, getting hit hard early and then started pitching better later, but just not good enough so far. I've got to start pitching better from here on out."
Opening Day Greinke allowed seven runs in four innings against the Rockies, and the Cubs didn't want to let him get settled in.
"We were going to try to be aggressive right out of the chute," Cubs first baseman Anthony Rizzo said.
The Cubs put together four straight hits in the first from Jason Heyward, Ben Zobrist, Rizzo and Kris Bryant, and then got a sacrifice fly to the wall in left from Miguel Montero to account for the runs.
"Made a bad pitch to Heyward, bad pitch to Zobrist," Greinke said. "Besides that all right, but Bryant hit his ball good. He's a good first-pitch hitter and I wasn't too upset about that pitch or the Rizzo at-bat, or the Montero one. You just can't have bad at-bats. Had two of them in a row to Heyward and Zobrist and just need to not do that."
After the first, though, Greinke seemed to find his rhythm a bit and he allowed just one more run -- thanks to a Zobrist RBI double in the fourth -- before departing after six innings.
"I thought he threw the ball well," D-backs manager Chip Hale said. "I think it's starting to come, starting to get comfortable. They jumped on him in the first inning. It happens a lot with good pitchers. They were swinging early in the count. Maybe a few pitches weren't where he wanted, but he hit some good pitches, too. I thought he did a good job. Got through the sixth inning, which was huge for us. Gave us a chance to win."
Greinke's next start is scheduled for Friday against the Padres in San Diego.