Houston finishes up a four-game series with the Dodgers on Thursday before traveling to Atlanta, Pittsburgh and Washington over the coming week and a half.
"When you're hired on, you're hired for 162 [games] minimum, and you go from there," Cooper said. "You rest in the winter. They've had their rest DH-ing and stuff. It's time to play baseball now. We've got to try to make up some ground."
The team will have a four-day break during the week of the All-Star Game, which will be played July 15 at Yankee Stadium in New York City.
But at least one Astro, first baseman Lance Berkman, will not get that four days of rest. He has run away with first place in the National League voting for his position. He will be practicing with the other All-Stars, while most of the league is resting up, and will have just one off-day after the game.
The Astros are currently fourth in the NL Central, 10 games behind the first-place Cubs. Cooper said they have a lot of work to do if they want to be in postseason contention in September.
"When you're in the race and you go up the hill and start coming down the other side, you better get the whip and start riding," he said. "We'll push them. We can't afford to back away."
Krysten Oliphant is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.