Ortiz went 1-for-3 with a second-inning double and a walk on Tuesday night.
"I thought his at-bats were OK," Francona said. "The biggest things for me was he didn't look frustrated."
Francona said Ortiz was as good in batting practice "as I've seen maybe in a couple years."
Ortiz was given the day off on Monday against Minnesota left-hander Francisco Liriano.
"We talked when we got [to Minneapolis], and I told him that I was probably going to do something," Francona said.
Ortiz has not batted anywhere but third in the Red Sox's lineup since May 13, 2005, when he batted cleanup against the Mariners. Not since May 2004 had Ortiz batted lower than fourth in the lineup.
"When you hit third, you must be swinging the bat good," Ortiz said. "I'm not, obviously. I'm moving to sixth, because we have guys who are going to bat good."
The move had been speculated about for weeks.
"It's probably a little anti-climactic for me," Francona said. "I've been thinking about doing some things."
Ortiz entered Tuesday's game batting .195 with a .299 slugging percentage. He had struck out 41 times in 154 at-bats while hitting only one home run.
"There's probably not a day that goes by that we don't talk," Francona said. "I wanted to just make sure that he understands the respect that we have for what he has done and what we think he is going to do. This does not change that. Sometimes you have to remind people of that, at least I think we should. I don't want him to feel like he's on an island here or anything like that, so that's why I decided to wait until we came here [to make a change]."
Will the pressure on Ortiz decrease as he bats lower?
"That would be the hope, that he doesn't feel like has to carry the team," Francona said. "There are times we are going to jump on his back and let him carry us for a couple weeks -- that's the kind of player he can be."
Francona added that "it's not as pronounced when somebody is hitting a little bit lower in the order, if they don't get hits."
"Quite frankly, I don't want to just shove him down in the eight hole," Francona said. "It's almost like placing blame. I just don't want to do that. I want to help him, or at least not be a hindrance to him getting hot."
Ortiz declined to comment prior to Tuesday's game and was short with the media afterward.
"I'm an employee," Ortiz said. "I follow orders."