In the long run I think Manchester City have a better chance at finishing top four ahead of Chelsea. Nottingham Forest are currently enjoying a fine run of form and not looking like they will slip up at any moment but if eventually something crazy happens then maybe Chelsea have a chance to catch up and replace Nottingham Forest in top four but until that happens, it’s still Liverpool, Arsenal, Nottingham Forest and Manchester City in top four.
I agree, now City will be able to rest more, since they are left without the Champions League, and we will see the team that we saw at the beginning of the season, when they could beat any opponent. Moreover, Guardiola will now make changes and they will sell some players, this should also create competition for a place in the starting lineup, which should also have a good effect on the results. City must get into the top 4, for them this is a mandatory condition for the end of this season.
Of course city May likely end in the top 4 this season depending on how consistant they're because newcastle is also trying so hard to make it up to the top 4 of the premier league table. Moreover, there is no point difference between the both teams manchester city is just topping newcastle with goals, so with this I think the possibility of manchester city ending in the top 4 this season is still under probability.