Laporte was carried off on a stretcher during Saturday's 4-0 Premier League win at home to Brighton after hurting his right knee in a mistimed challenge on Adam Webster.
The seriousness of the injury is still being assessed with a full diagnosis expected in the coming days but Pep Guardiola admitted after the game that he feared the defender will be out “for a while”.
City will already be without winger Leroy Sane for at least six months after he ruptured his cruciate knee ligaments in the Community Shield in August and Rodri is hoping that Laporte’s injury is not as bad.
“It looked serious, that's why we are not very happy,” the midfielder said. “He's a very important player for the team and it's going to be tough without him.
“We've lost two big players. Leroy and now Aymer. It doesn't look very good but let's see what it is. And then we have to keep on working.
“This is football, this is how it works but I think we have enough in the team to cope with it.
“We have to support our team-mate, we hope he's going to be back soon and we have to stay together to fix this kind of moment."
City are short of cover at centre-back following Vincent Kompany’s exit in the summer but will have John Stones back after the international break after missing three games with a thigh strain.
With Nicolas Otamendi the only other senior centre-back available, Guardiola will use midfielder Fernandinho as an extra option.
That option is helped by the successful start made by Rodri, who has slotted into the holding midfield role following his €70 million (£63m/$79m) move from Atletico Madrid in the summer.
"It's great to have team-mates who can adapt to other positions. Fernandinho is a great player, he can play also as a centre-back,” Rodri added.
“He's done very well there, he was great [against Brighton]. And he took on the responsibility to take the ball, so it's good for the team.
“For me it was not easy at first, there were some difficult moments. I never played in these types of games before - with so many transitions. But I will get used to it and will adapt.
"It's a big difference, many times the matches you are playing box-to-box and you have to be smart. We have a good team and I’m working on it."