Stanford was staying with Missouri despite giving the 13th-ranked Tigers plenty of extra opportunities to score.
The Cardinal gave up 19 offensive rebounds in the 78-70 loss to Missouri on Thursday in the opening round of the Battle 4 Atlantis.
"I am proud of my guys. I thought we went out and competed well," Stanford coach Johnny Dawkins said. "We could have executed a little bit better. I thought defensively, we could have been better as well.
"Nineteen offensive rebounds are way too many to give up. A lot of them were us making a good play and didn't rotate as well as we needed to on the backside. We have to be more aware of those situations and look at making multiple plays in order to secure the ball."
Laurence Bowers scored 19 points, as usual most were in the second half, and grabbed 10 rebounds for the Tigers.
Bowers, who had 13 points in the second half Thursday, has scored more points after halftime in every game this season for the Tigers (4-0). He came in averaging 15.5 points, 14.0 in the second half.
"Second half is when you put the team away," Bowers said. "On an individual standpoint, I would love to play better in the first half, but whenever I get the opportunity to step up for my team, that is what I am going to do. And if that is in the second half, I am going to try and continue to do that."
Missouri will face the winner of the first-round game between No. 2 Louisville and Northern Iowa in Friday's semifinals.
Phil Pressey had 18 points and eight assists for Missouri, which had just three field goals over the final 9:10 and they were all grouped in a 1:57 span starting with 2:12 to play. It didn't matter as the Tigers were 10 of 11 from the free throw line over that span. They were 22 for 25 for the game.
"When you have your big men make free throws, that is key," said Pressey, who made all six of his free throws. "When Alex (Oriakhi) makes his free throws and your guards, that is a given — they have to make their free throws, overall that just helps you out."
Bowers missed last season with a torn knee ligament.
"I am definitely getting better day by day, both physically and mentally," Bowers said. "Taking hard hits or anytime I end up on the ground that just builds my confidence that much more on my knee.
"I am very comfortable with Phil Pressey on the floor and think our chemistry is coming along greatly and with the other guys as well. I just have to get better with progression day by day."
Chasson Randle had 22 points for the Cardinal (3-2), who have lost two straight after an eight-game winning streak.
"They made a lot of plays when it counted — a lot of offensive rebound putbacks, beat us to loose balls," Dawkins said. "They did a good job in those areas."
Missouri finished with a 43-39 rebound advantage including 19-12 on the offensive end.
"I thought it was a very physical game and thought we responded very well after the first part of the game," Missouri coach Frank Haith said. "We had some guys make some big plays down the stretch.
"Rebounding and defense is a big part of who this team is. I thought we did that much better in the second half and were able to come out with a win."
Stanford, which trailed by 12 points in the first half, stayed within reach in the second half and was down 72-68 with 1:15 left on a long jumper by John Gage.
Pressey took over from there, scoring the Tigers' last four points and assisting on the two before that.
Oriakhi, who played in this tournament last season with Connecticut, had 13 points for Missouri. Oriakhi transferred after the season and did not have sit out a season because Connecticut was put on probation.
Earnest Ross had 10 points and 11 rebounds for the Tigers but he was 3 for 19 from the field and missed all five 3-point attempts.
Missouri shot 36.6 percent from the field, just 31.9 percent in the second half.
"When your shots don't fall, that doesn't mean you can't win," Haith said. "You have to find a way."
Dwight Powell had 18 points and 10 rebounds for the Cardinal while Gage added 10 points.
"It definitely was a physical game. We learned a lot from it," Powell said. "Those guys competed hard especially offensively and showed us that we have to have five guys rebound and we cannot allow them to bully us underneath like they did today. Something we can definitely improve on."
Randle was coming off a 2-for-16 effort from 3-point range in the loss to Belmont and he was 1 of 6 from there against Missouri. The Cardinal were 6 for 26 from beyond the arc while Missouri was 4 of 19.