Not going to make a single difference IMO.
The only way we will lose out on players is if they fancy moving to Barca, Bayern or Madrid, something which wouldn't have changed even if we were in the CL. The though that players would suddenly prefer to sign a 5 year deal at United or Leicester just because they have CL football this season is laughable.
We will still match the pay scale and have a clear plan of how this club will progress. No player will seriously look at City and think that they are a club on the decline. They will see a club who have had a poor season and are about to embark on the next stage with the most sought after coach in the world in charge.