Story has homered six times, including twice in two of the games. But it ended Saturday, when he went 1-for-5 with three strikeouts.
"I enjoyed it -- mostly, the games we won," Story said. "I didn't enjoy it that much when we lost. It was cool.
"I wouldn't say that I was putting pressure on myself to do that. [But] it's kind of a relief."
Story, batting second -- behind either Charlie Blackmon or DJ LeMahieu and ahead of Carlos Gonzalez -- is hitting .333 (8-for-24) with two singles and 11 RBIs. He'll go down in history with Willie Mays (1971), Mark McGwire (1998), Nelson Cruz (2011) and Chris Davis (2013) to homer in the first four games of a season.
Story's two homers Monday at Arizona established a first for a player making his Major League debut in an opener.
"I'm not sure, he'd probably like to hit a homer every game," Rockies manager Walt Weiss said. "But it's a heck of a run."
But the Rockies are 2-3, and that record is the one on Story's mind.
"That's what it's all about," he said. "Personal achievements are cool and everything. But that's not why we're here. We're here to win. If we don't do the job that night, then we're not very happy."
Thomas Harding is a reporter for MLB.com. Read his blog, Hardball in the Rockies, follow him on Twitter @harding_at_mlb, and like his Facebook page, Thomas Harding and Friends at www.Rockies.com. This story was not subject to the approval of Major League Baseball or its clubs.