Pep Guardiola’s men turned on the style in the second half to earn a deserved three points on the south coast.
However, despite enjoying large spells of possession and carving out several decent chances, it took a typically inch-perfect cross into the box by Kevin De Bruyne and powerful Erling Haaland header on the stroke of half time for City to find the breakthrough.
This led the charge to then finish the match on a high, including a second goal for the Norwegian, as well as strikes for Grealish and Alvarez. De Bruyne also tallied his 100th Premier League assist.
And while Rodrigo was impressed by City’s performance after the break, he believes there’s still room for improvement ahead of Bayern Munich’s visit on Tuesday.
Reflecting on the win over Southampton, the midfielder said: “We came here to win, and we won it. I think we struggled a little bit in the first half – the first 20 minutes weren’t very good.
“We struggled a little bit to find the spaces. The goal made us calm for the second half and gave us confidence and we played much better.
“It was important because we weren’t as strong and aggressive as we were in the second half. We were a bit slow and needed to move the ball quicker.
“Looking ahead to the Bayern game we have to start better and be more aggressive. We’re on a great run and we want to keep it going.”
City host the Bundesliga champions on Tuesday 11 April, with kick-off scheduled for 20:00 (UK).
The Spanish midfielder knows that City will need to be at our best to begin the first of the two legs on the front foot.
“We look ahead with a lot of emotion and happiness to want to face them,” began Rodri. “A big, big rival in Europe and we will have to show the best of ourselves if we want to have a chance against them. We have to fix some things.”
Rodrigo also reflected on having two team-mates in great form ahead of the Champions League clash – Erling Haaland and Jack Grealish.
For the Spanish international, the City duo are both performing at the top of their game at a crucial part of the season.
He said: “In terms of goals, he’s [Haaland] been a beast this season. He does a lot – we have pace and a lot of danger in the area. He’s a special guy.
“These kinds of players can make the difference at any time. He has the ability and talent to do this.”
“[Jack is] in a big moment right now. He’s making another step forward with assists and goals which is great for the team.”