Last season's Champions League semi-finalists lost 2-1 at home and finished with 10 men in the first leg, then had another three sent off as they could only draw the return 1-1 on Saturday.
"We are out (of Europe) because we played with fewer players in both encounters and because our rivals were very motivated. They were deserved winners," Pellegrini said.
"You cannot afford to have four players sent off in two games. I am really annoyed."
Striker Diego Forlan, midfielder Alessio Tacchinardi and defender Gonzalo Rodriguez were all shown red cards near the end of Saturday's game. The side played 43 minutes of the first leg with 10 men following Josemi's sending off.
Villarreal fell to Arsenal in last seasons Champions League semi-final. They reached the UEFA Cup quarter-finals in 2005 and the semi-finals in 2004.
Maribor progress into the second qualifying round for the UEFA Cup.