If you enter the Premier League with the intention of failing to put out the necessary effort and concentration, you should not be far from being demoted. The Premier League is not for the faint of heart and has humbled many clubs. And many respected clubs, including Chelsea, have struggled this season. One characteristic of these leagues is that weaknesses in your defense or midfield can have a bigger impact than you might assume. Since there are many rivals in the tournament, you need to significantly improve performance to remain in the Premier. This requires more expertise than you might think.
I don't know of any team that would come into the premier league or any league at all and won't be ready or willing to put in efforts towards some goal and most of all, not being relegated. Your always going to find teams that won't meet the requirements in there efforts to remain in the league.
Chelsea had the determination but, they just weren't being able to find the goals. They had attempts but, a very poor conversion rate with no proper goal scorer on the team.
They were just lucky not to get relegated.