Betis claimed a 2-1 home win over Elche, with Pablo Fornals scoring a 68th-minute winner, to book their spot in Europe's top competition for the first time since the 2005-06 season.
They have been regulars in European competition in recent years, qualifying every season since 2021 and reaching the Conference League final against Chelsea last season.
"It’s not easy to be in European competitions for six years, much less to have qualified for the Champions League two matches before the end of the season,” Pellegrini, 72, told reporters.
"The team’s greatest merit was always getting back up after losing. I think all those stumbles were more than compensated for today with the great celebration we had in our stadium, with our fans, to whom we owed this joy," he continued.
"We started the first match of the season against Elche, and at the end of the team talk, we wrote in green letters, 'Today we begin our journey to the Champions League.'"
Betis next face newly-crowned LaLiga champions Barcelona on Sunday.