Bullock, a fifth-round draft pick out of Texas A&M, was competing with veteran Shayne Graham. Bullock was 3 for 4 on field goals and Graham has gone 5 for 5 in the preseason.
Kubiak said Sunday that Bullock's groin "had been bothering him" in recent weeks and he had played through it. Bullock was "black and blue" and could barely lift his right leg, Kubiak said, when he came into Reliant Stadium for treatment following Saturday's 34-27 loss in New Orleans. He will go on injured reserve.
"A sad situation," Kubiak said. "He's going to kick in this league, he's going to kick a long time. Thankfully, we have Shayne, who's done a hell of a job, too."
Graham, 34, is entering his 12th season. He's bounced around the league as an injury replacement following seven years in Cincinnati, which included a Pro Bowl spot in 2005. He went 12 for 12 for New England in 2010 after Stephen Gostowski went on injured reserve with a thigh injury, and kicked briefly for Miami and Baltimore last season.
Graham is 145 for 157 on field-goal attempts inside 40 yards since 2001.
"I think we would've been proud with either one of them," Kubiak said. "I think this situation obviously calls for Shayne to move forward and be our guy. We expect him to do well."
The Texans (No. 6 in the AP Pro32) wrap up the preseason against Minnesota (No. 29) on Thursday night.
Kubiak said center Chris Myers and star receiver Andre Johnson were "both fine" after leaving the game early against the Saints. He said nose tackle Shaun Cody (back) and defensive end J.J. Watt (dislocated left elbow) will both practice this week, but won't play against the Vikings.
Kubiak says he'll decide later whether backup quarterback T.J. Yates will play on Thursday night. Yates, pressed into duty last season following injuries to Matt Schaub and Matt Leinart, is 19 for 32 in the preseason. Veteran John Beck and undrafted rookie Case Keenum are competing for the No. 3 spot on the depth chart at quarterback.
"I've got a decision to make there," Kubiak said.
Yates may get some playing time, because Kubiak wants to see improvement from the second-team offense. Yates went 6 for 11 for 72 yards and was sacked in New Orleans.
"The last two weeks, it's not been very good," Kubiak said. "We struggled up front with some issues, some protection schemes and stuff. In a lot of ways, T.J., he didn't play with the confidence that he normally plays with back there."
Kick returner Trindon Holliday and rookie receiver Keshawn Martin both fumbled twice in New Orleans. The 5-foot-5 Holliday shined in the first two preseason games, returning a kickoff 90 yards for a touchdown in the opener, then running back a punt 87 yards for another score in the second. He atoned for the miscues in New Orleans with a 62-yard kickoff return, but Kubiak says he's still hasn't decided whether to keep Holliday on the final roster just to return kicks.
"I've been very pleased with what Trindon has done, but he can't turn the ball over," Kubiak said. "The question is going to be, when we go and set this roster next week, we've got to look at the big picture. Is there a room for just a returner? That question is not going away."
Martin, a fourth-round draft pick, finished his college career at Michigan State ranked second in punt return yards (659) and eighth in kick return yards (1,100). Kubiak said Holliday will field all the kicks on Thursday night, but he's also confident that Martin and safeties Shiloh Keo and Danieal Manning could also handle kick-return duties.
Manning has averaged 27 yards per return in 114 attempts since 2006, the second-highest average since that year.
"Danieal Manning, to me, could be the best kick returner in football if we let him do it," Kubiak said.
Kubiak is also still keeping a close eye on the competition between offensive linemen Derek Newton and Rashad Butler. Newton started against the Saints.
"I think it's been a very good battle," Kubiak said. "I think I'll settle down on that, make a decision here in the next day or so before we get onto Thursday. They both continued to do good things, but nothing's perfect yet, obviously."
Kubiak also said Sunday that linebacker Darryl Sharpton will go on the physically unable to perform (PUP) list as he continues to nurse a quadriceps injury.