Ronaldo won and converted the second half spot-kick that gave Rangnick a second successive Premier League victory since he replaced the sacked Ole Gunnar Solskjaer.
United found it difficult to impose themselves for long periods and it took several fine saves from David de Gea to keep them on level terms before Ronaldo's 13th goal since rejoining the club from Juventus in August.
"It was a very intense game, very physical," Rangnick said. "We need to be able to compete on that kind of level. There's still room for improvement in this area.
"The second half was a little bit better but at the end we were lucky to have a clean sheet. It's another clean sheet but still a lot of work to do.
"It's also a question of body language and physicality and this was one of the major issues that we could have done better."
Rangnick's side sit in fifth place in the Premier League, level on points with fourth-placed West Ham, as the German aims to haul his club back into the Champions League places.
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While United must improve significantly on this mediocre display against the Premier League's bottom club, Rangnick will take heart from successive clean sheets -- a stark contrast to the woeful defending seen in the 4-1 loss at Watford that ended Solskjaer's reign.
Rangnick, who kept faith with the team that beat Crystal Palace 1-0 in his first match last weekend, wants to introduce a high-tempo pressing style to United.
But after making 11 changes from the midweek Champions League draw with Young Boys, there was a noticable lack of energy about United at times.
Norwich were without several players after boss Dean Smith hinted at coronavirus concerns in the squad on Friday, but they still matched United stride for stride.
United were inches away from an early lead when Alex Telles' free-kick deflected off the Norwich wall and cannoned off the crossbar.