Betis had the lead through Ez Abde, before Chelsea stormed back to win through goals from Enzo Fernandez, Nicolas Jackson, Jadon Sancho and Moises Caicedo all after halftime.
Pellegrini said afterwards: "What happened in the second half? We played a great first half; we scored a goal, we had a couple more clear chances, but in the second half we were affected by injuries.
"The fans have been incredible, during the game and even after. This is what hurts us most: not being able to give them this title.
"We have qualified for Europe next season but I have to say injuries today really caused us problems. Against a team as powerful as Chelsea, that's always going to hurt you.
"How do the players feel? They are devastated. We couldn't maintain what we did in the first half."