They beat French side Rennes 3-0 on Thursday to advance 4-3 on aggregate to the quarter-finals of Europe’s second-tier club competition.
Pierre-Emerick Aubameyang struck either side of an Ainsley Maitland-Niles goal as the North London side joined local rivals Chelsea.
Arsenal became only the second team in Europa League history to win a tie after losing the first leg 3-1.
“This comeback was very difficult, but I think the reaction was very good from every player,” Emery told reporters.
“We can be proud of our players today because it was a very difficult week — (Manchester) United on Sunday and today against Rennes.”
Arsenal’s 2-0 home English Premier League (EPL) win over Manchester United on Sunday kept alive their hopes of a top-four finish and a place in the UEFA Champions League next season.
“Playing under pressure is good, growing up under pressure — with each player playing like a team and feeling the difficult moments to give us our best performance,” Emery said.
Arsenal have missed out on UEFA Champions League football for the last two seasons, and their poor away record remains a big concern.
Although they have no more top-six teams to face in the EPL this season, they play more away than home fixtures.
Nevertheless, Emery said the UEFA Champions League, Europe’s premier club competition, was not his only focus.
The Europa League — which he won three times in a row from 2014 to 2016 as manager of Sevilla — also provides the chance for silverware.
“I said to the players today (Thursday), I’m excited (about) this competition, but it’s exciting not only for the possibility to go to the UEFA Champions League, but also because it’s one title,” he said.
He also took note of surprising results elsewhere.
“Today (Thursday), Inter (Milan) are out, Sevilla are out — a big surprise. And the last teams, they are all very important, and it’s going to be very difficult,” Emery said.
For his side, the focus must always be simple.
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