The Gunners edged past Middlesbrough 2-1 tonight at the Riverside in a must-win game.
Alexis Sanchez and Mesut Ozil found the net to keep fans hoping of an unlikely push for Champions League football.
Arsenal are now up to sixth and seven points behind fourth-placed Manchester City, although they do have a game in hand.
Having achieved what they needed to against Boro, Wenger is now focusing attention back on the FA Cup.
Arsene Wenger is still pushing for Champions League qualification at Arsenal Arsenal player ratings against Middlesbrough Mon, April 17, 2017
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Petr Cech – 7: Made a crucial save when the defence failed him
It [the top four] is mathematically still alive
Arsenal face City at Wembley on Sunday (3pm), where the Frenchman’s players can earn a small break mentally from the pressures of Premier League progress.
However, with Leicester visiting the Emirates three days after the semi-final, Wenger is ready for the challenges ahead.
"It [the top four] is mathematically still alive,” Wenger said.
“We knew we needed to win.
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“Now we have a little break with the FA Cup and then we come back again to the league."
Arsenal still have seven league games left due to their backlog of fixtures.
With no announcement made yet over Wenger’s future, the Gunners’ success in the run-in could prove crucial.