No one is underestimating City, and they need to fight for their survival in UCL for us to confirm that they are worth to qualify for the round of 16. Same applies to EPL, despite being the defending champions does not mean that if they don't improve their performance, they will be able to finish on top four. City have only won two weak teams and no one knows if they have improved or not.
Pep will continue to move to make improvements to the Manchester City team as time goes by because he himself is also very frustrated when the team he coaches gets bad results. So I also think that Pep will try to stay in the Champions League and also try to get a position in the top four zone in the EPL this season, although some other teams in the EPL will also try to take one of the positions in that zone. But for now Manchester City are not too far away from being able to achieve that although they have to fight harder.
Although Manchester City did not qualify for the UCL next season, Pep Guardiola position will remain as a coach. We all know that there will always be a time when someone era ends and Pep Guardiola cannot avoid it. Meanwhile Manchester City's top brass also cannot hide their frustration, because from the beginning they did not plan a replacement coach, whether they like it or not they will continue to force Pep Guardiola. Manchester City's portion to reach the peak of the Champions League final this season is getting thinner.