The Ligue 1 side built a 3-1 lead in last week's opening leg but Pierre-Emerick Aubameyang recorded two goals and an assist in Thursday's return at Emirates Stadium to send the Gunners through 4-3 on aggregate.
That 3-0 victory followed a 2-0 home win against Manchester United in the Premier League on Sunday, with Emery's men inflicting the first domestic defeat of Ole Gunnar Solskjaer's temporary spell in charge.
Arsenal are fourth in the Premier League table, holding the final Champions League qualification place, although triumphing in the Europa League offers another potential route back into the continent's elite.
And with Arsenal showing more consistency following the turbulent early months of his reign after replacing Arsene Wenger, Emery feels his team are on the right track after a sixth straight home victory in all competitions.
"For us, today and Sunday we were competitive. I think it's good confidence for us to feel that," Emery told a news conference.
"After, I want to take to take better control with the ball and with possession. Against United and today we lost the ball a bit.
"We are going to continue working next week, we are going to Dubai. We have good possibilities in the next month to do something important.
"We can be proud today. Very difficult week, United on Sunday and Rennes today. Today we played very consistent, being competitive without the ball and serious defensively.
"I missed us being a bit more controlled with the ball, but they left a lot of attacking players in the final third which gave us space to attack them. Our match was competitive, we did well today."
Premier League clubs make up four of the Champions League quarter-finalists with London rivals Chelsea joining the Gunners in the Europa League's last eight.
Emery led Sevilla to three consecutive Europa League titles but the Spaniard is unsure whether Arsenal can be considered favourites to lift the trophy in Baku in May.
"These two matches have been very difficult," Emery added. "Today, Sevilla are out, Inter are out. Every team is now important and it's going to be very difficult.
"The Champions League and Europa League have different moments, sometimes Spanish clubs, English clubs [do well].
"A domestic league like here [the Premier League], we have six teams playing for the top four.
"I said to the players this competition is exciting not just because it gets in the Champions League, but also it's a title."
Arsenal return to action at home to Newcastle United on April 1.