With two out in the fifth and facing slumping Andre Ethier, Cook threw four straight balls to load the bases. Casey Blake followed with a three-run double -- the big hit in the Dodgers' 7-1 victory at Coors Field in front of 25,384.
Otherwise, it was another strong outing from Cook (3-2), but in the end, he gave up five runs (four earned) and eight hits in six innings. The Rockies are 1-7 against the Dodgers and 13 games behind them in the National League West.
"I felt like I made about four bad pitches, and the four bad pitches, they hurt us," said Cook, who threw his first career shutout in his last start. "When a team's doing that, it makes it real tough. You've got to be so precise."
The Rockies dropped to nine games below .500, matching their season worst. The Rockies came off a 5-5 road trip hoping to make a move at home. Instead, they head into Wednesday afternoon's finale of a three-game set trying to avoid being swept.
The Rockies, who are 7-12 at Coors Field, entered the season expecting to compete with the defending NL West champion Dodgers, who have gone 11-7 since star outfielder Manny Ramirez was suspended for 50 games under baseball's policy against performance-enhancing drugs.
"We haven't showed up as well as we'd have liked against them," Rockies manager Clint Hurdle said. "We're six games under against them, and we're nine under for the season. We just haven't matched up well against them."
Cook (3-2), whose throwing error led to a first-inning run, walked just three in six innings. Two were understandable. They were to Orlando Hudson, who nonetheless extended his hitting streak to 16 games with a third-inning single.
Cook walked Hudson just before facing Ethier, who at the time was in a 2-for-19 skid. The double by Blake, who is tied with James Loney for the Dodgers' lead in RBIs at 32, gave the Dodgers a 4-0 lead.
"Not even a full half-inning," Hurdle said. "I mean, he rolled 15 ground-ball outs.
"There were a lot of quick outs, a lot of soft contact. But that inning, for a about 10-15 pitches, he couldn't get anything where he wanted."
Clint Barmes homered off Eric Milton (1-0) to lead off the bottom of the fifth.
However, Milton, in his second start of the season, earned his first victory since Aug. 8, 2006, before missing most of two years because of Tommy John elbow-ligament transfer surgery. Milton gave up seven hits in five innings, but didn't walk any, struck out three and changed speeds well enough to be effective.
It's an old story for the Rockies, who went 0-for-10 with runners in scoring position. They played without team RBI leader Brad Hawpe (36), who was resting a sore right groin. Barmes kicked himself for missing a good pitch and flying out to center with two on in the second inning.
"It just seems like that's the way it's been," Barmes said. "We get runners in scoring position, and it seems Hawpe's the only one that comes to mind that's really been knocking guys in. We definitely need more guys to step up and knock guys in."
Juan Pierre tripled off Cook and scored on Hudson's second single of the game in the seventh. Pierre added a two-run single off Jason Grilli in the eighth.
Thomas Harding is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.