Pep Guardiola’s side fully deserved our two-goal lead to take back to the Etihad Stadium after a strong performance in the Champions League last-16 first leg in Denmark.
But Grealish looked dejected when he was forced off in the 21st minute with what looked like a groin strain while Bernardo was left limping after a strong challenge late in the game.
“Bernardo has a big knock in his ankle,” Guardiola said.
“I didn’t speak to the doctor but it looks like muscular for Jack.
“In the last few days his mood in training sessions was much better. He was really good, he help us to play in the right tempo especially in the first leg.
“You cannot play so slow but you cannot play so fast. Against teams that are incredibly organised you have to find the right moment and play the right tempo. Jack help us a lot and hopefully he will recover quickly.
“He wanted to continue but we are not going to do more damage.”
It was a niggly game with plenty of fouls but Guardiola said Spanish referee Jose Maria Sanchez handled the game well.
“Every time you come here they are so aggressive and we have to handle it,” he added. “The referee did a good job - they have to manage that.
“Hopefully Bernardo is not a big issue. In a few days we have Chelsea at home and we have to recover as quickly as possible.”
After having a full squad to pick from recently, City have suffered a couple of injury setbacks with Josko Gvardiol and Mateo Kovacic both missing the trip to Denmark and Guardiola gave an update on their fitness.
“Josko [will be] two weeks or three weeks,” he said. “He has [a problem with a ligament] in his ankle.
“Kova is in the process to come back. Thursday or Friday he will train with us and we will see how he feels.
“Unfortunately, now with the schedule we have we need players fit and every game and training session we lose players and that is not good.”