The decisive goal of the tie was scored by Abde Ezzalzouli in the first half of extra-time as the Spanish club secured a 2-2 in the second-leg in Italy after a 2-1 at home last week.
While being happy to give the club's fans immense joy, Pellegrini quickly turned his attention back to the league, stressing that securing a Champions League spot in LaLiga remains his top priority.
Betis are currently sixth in the standings, four points behind fourth-placed Athletic Bilboa who sit on the final Champions League qualification position.
"My satisfaction is logical. It makes me much happier to see the joy of the Betis fans. We felt a little bit indebted, with the need to give the Betis fans this kind of joy.
"From tomorrow we leave the Conference League out because we have four very important league games left to aim for the Champions League until the end of the season."
Whatever happens in the league though, Betis can look forward to a European final later this month where they will take on English Premier League side Chelsea.
Pellegrini added: "We are very happy to reach the final, and even more so with Chelsea and I sent (manager Enzo) Maresca a message a long time ago being very happy for him."
Chelsea have booked their spot in the UEFA Conference League final, setting up a showdown with Real Betis later this month, after a composed and confident performance saw them ease past Djurgarden 5-1 on aggregate.
Brazilian winger Antony has hailed his January loan move to Real Betis as the best decision he's ever made, after a difficult stint at Manchester United.
Real Betis brought the heat once again in Europe, continuing their red-hot run by taking down Polish underdogs Jagiellonia 2-0 in Seville to seize the upper hand in their UEFA Conference League quarterfinal tie.
Real Betis CEO Ramon Alarcon has expressed a growing sense of optimism about the possibility of keeping Manchester United winger Antony beyond this season.
