Sergio Ramos labelled it "mission accomplished" after Real Madrid sealed top spot in Champions League Group G.
Goals from Gareth Bale and Lucas Vazquez earned a 2-0 win at Roma as Real recovered from the embarrassing LaLiga reverse at Eibar.
"Mission accomplished: qualified and top of the group," Ramos wrote on Twitter.
Real Madrid head coach Santiago Solari now has two wins from his two Champions League games in charge and was pleased with the victory.
He said on uefa.com: "The players showed they can take responsibility and we're really happy to get the win.
"We had to work hard and suffer, but sometimes that's just what you need to do and we won playing like that.
"We worked hard throughout and in football that's what you need to do. Games are 90 minutes long and you have to grow into them sometimes."
Bale netted his 20th goal in 58 Champions League appearances, punishing a poor clearance from Robin Olsen and a misjudged header from Federico Fazio.
The Welshman said: "We like playing against the best and this brings out the best in us.
"The objective is to keep improving. Obviously we've got a new manager so it's going to take a little bit of time, but we just have to keep proving everybody wrong and fighting for each other."
Cengiz Under spurned a golden opportunity to give Roma a half-time lead and the hosts were left to rue the miss from close range.
Roma coach Eusebio Di Francesco said: "We're playing against a side of champions and the difference can be seen when they score with their first chance."
Nicolo Zaniolo added on asroma.com: "We didn't take our chances and they did – when they had an opening they took advantage. We missed our chances and they didn't. We need to be better in front of goal."
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