Rodri is in Barcelona waiting for a second opinion on the knee injury sustained during Sunday's draw against Arsenal but City fear he could miss the season.
Guardiola admitted that the 28-year-old will be missing for an extended period but that he will find ways of softening the blow.
'Still we don't have the definitive, but he will be out for a long time, a while, but maybe it will be less than we expected,' Guardiola said.
'I cannot tell you because we are waiting on the phone calls from him and the doctors to know exactly what he has and the type of surgery he has to get. I think tonight, tomorrow we will know.
'We don't want it, but we will still have a good season. I trust a lot in my players. I have a duty to find a solution.
'Rodri is irreplaceable and the team won't play with the best midfielder in the world for a long, long time. Of course it's a big, big blow for us.
'It's football, it's happened, and my duty is to find a solution, to be competitive like we have been for many years.
'Rodri is not here, it's a problem. But complain? I feel sorry for him. Recover best as possible, we wait for you, and go for it. This is the challenge. Go to Newcastle, try to win, do what we have done for many years. Simple as that.'
Guardiola also revealed that he messaged Mikel Arteta amid the fallout of City's draw with the Gunners – and claimed his former assistant's tactical set-up was nothing new.
Guardiola revealed that he told Mikel Arteta that 'they did amazing' despite criticism from the City players toward Arsenal's tactics
'It's fine, they were brilliant,' the City boss added. 'I admire what they have done, I cannot do that with my team.
'I said to Mikel, they did amazing, not a problem. They know their players and do what they have to do.
'The opponents can play how they want to. Up to us to handle them. We play a lot of teams defensively. Do you know how many times teams play like that? Millions. It's about us.'