Despite securing a 3-1 victory, destiny was out of Arsenal's hands due to results elsewhere on the final day as wins for Liverpool and Manchester City ultimately brought an end to the club's hopes of competing in the world's most lucrative club competition next season.
Instead, Arsenal's fifth-place finish will see the north London outfit compete in the Europa League - a competition that hasn't featured the Gunners since 2000 when the Premier League side fell to Galatasaray in the UEFA Cup final.
Collecting three points, however, was overshadowed by disappointment in the stands as supporters directed their frustration toward owner Stan Kroenke, who reportedly turned down a £1-billion offer to sell his majority share in the team.
"I respect Stan Kroenke a lot," Wenger told reporters after the match. "He's not at fault for us missing the Champions League. The technical department is responsible for that."
Arsenal secured the victory with just 10 men following Laurent Koscielny's straight red card for his reckless challenge on Enner Valencia in the first half. The unnecessary lunge and subsequent red card will force Arsenal to compete in next weekend's FA Cup final without the French international.
With Koscielny ruled out, manager Arsene Wenger could face another headache heading into the FA Cup final after Gabriel Paulista was forced to leave Sunday's contest when his knee appeared to twist awkwardly during a sliding challenge.
Relegation to an inferior tournament comes with financial consequences, but the ripple effect of missing out on the Champions League could harm Arsenal's effort to attract players this summer, as well as having negative consequences during the team's effort to convince Alexis Sanchez and Mesut Ozil to sign new contracts.