In order to make the Europa League attractive, it shows up in the Champions League, which is the champion of the Europa League, apart from that, there is nothing attractive for big clubs. In addition, big clubs are already participating in the Champions League by becoming champions in their own leagues or by entering the top 3-4. The Europa league and the later conference league (formerly the cup winners' cup) is an attractive destination for medium-sized and small cubes in Europe. If these tournaments had bigger sponsors and bigger prizes, I'm sure the big teams that were eliminated from the Champions League would fight here as well. Football is no longer entertainment, it's a big economy for clubs and countries.
Considering there are many clubs whose entire roster cost about 10-20 million, it is important to note that being at a good stage in europa or conference cup would be a great big deal for them. They could make millions, and spending millions to get better.
Look at Sherrif and last year and also this year, they were already good in their own league, and they made so much money in the past 2 years that I am pretty sure they will stay the best team of their nation for a long time thanks to all that money unless they spend it on players turn out to be horrible. Maybe big clubs do not care, but smaller clubs do. Big clubs only would want to win if they are there because they like winning, not because of money or fame or anything, but winning is the aim after all.