Ronaldo also had a goal disallowed for offside as he moved to 18 Premier League goals for the season.
The result means United remain in the chase for fourth-place, although they are still five points behind Arsenal, who have two games in hand.
Speaking to Sky Sports after the game, Rangnick said: "We were in control for most parts. In possession that was one of our best performances this year. It was the type of performance we wanted to show to our supporters.
"We played with Juan Mata and Nemanja Matic and that gave us some quality in midfield. It was not too easy for Brentford to take the ball away from us. In the first half we played too many square and back passes but in general it was a good performance.
"In the end I'm not happy with the results [overall], especially in the last four or five weeks. Until the West Ham game we were still in the race in three competitions. We had good moments until that West Ham game, we conceded fewer goals but in the last few weeks performances have not been as good as they should have been. In general we have lacked consistency."
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