It's not that easy to win Champions League so I am not sure about Liverpool running favourites but given how Liverpool plays one would have hope for them to qualify for CL at least. This season didn't went according to plans and I feel like there were lot of factors behind it.
They got affected by two seasons ago when they tried to have a treble or four titles in that season. Probably their players got tired in the past season as some of effects from two seasons ago, hence they got more injuries and played worse. It can be coincidence or can be real reason for Liverpool performance in the past season.
I think for upcoming season they would hope for top 4 finish at least. About Europa, it does seems Liverpool, Brighton and Roma would be the favourites but transfer window is still open and we could see lot of crucial players move out still. Let's see how the squad shapes up after the summer transfer window.
They can play better but they will have more challenge from Newcastle United. Premier League now are more tough with rising clubs like Arsenal and Newcastle United. Manchester United and Chelsea are other clubs will compete for top four with Liverpool, together with Manchester City. Together we will have 6 clubs compete for 4 positions and if we count Tottenham Hotspur, it will be 7 clubs.