I've recently yoyoed between having brilliant seasons where I've been out the CL and had a storming league season (and often a good cup run to boot) and dire league campaigns when I've qualified for the CL. My take on your question is that when you are in three competitions the toll on your overall squad is much higher, and with the necessity to rotate players with two games a day you will undoubtedly end up playing a few players who are having a 'bad' season. The impact on your results can be quite dramatic - I won every game in the CL group stage last season but nose dived down the league to finish 8th as I was relying on 'bad season' players to come in and do a job.
I guess you need to do one of the following - suss out quickly who are your most consistent 15-16 players currently and prioritize one competition, playing a solid team most matches OR be very active in the transfer market, root out the 'bad' players in your squad and replace them early in the season when they show signs of tanking. The latter option will require stacks of cash (and probably tokens too) plus a lot of luck to sustain serious challenges in two/three comps the higher up the league system you go.