Focusing on one of them might actually be quite good. But I think Jurgen Klopp can divide his focus between the two, namely the Premier League and the European League. Because Man City can also do it, Liverpool can definitely do it too. Even Man City is also dividing its focus with more competitions such as the FA Cup, UCL and Premier League. So Klopp's task actually didn't become more complicated after Liverpool were eliminated from the FA Cup. He just has to try to stay consistent in the Premier League and then he also has to keep going further in the Europa League. The match schedules are not that close together. So I think the squad that Liverpool currently has is enough to be able to perform optimally in both competitions. It's just that I agree that Leverkusen is the real challenge in the Europa League. Liverpool must hope not to meet Leverkusen early.
Liverpool and Klopp will be same like Manchester City and Pep Guardiola. They will both try to win Premier League and Europa League (Liverpool) and Champions League (Manchester City). At this time, they will not try to decide what competition is most important for them as both titles are big ones and they still have due chances to win both titles.
Manchester City look to have better player resource and don't have problems with player injuries at this time and it's big advantage for them in their race directly against Liverpool in Premier League. The wave of player injuries can affect Liverpool performances in coming matches and can affect their endings this season.