Wenger confirmed in April that his 22-year association with the club will conclude at the end of the season and the players' bid to see him sign off with a first European trophy ultimately came up short against Diego Simeone's characteristically shrewd Atletico, for which Diego Costa netted the decisive goal.
Arsenal's luck appeared to be out early on as it lost captain Laurent Koscielny to injury, with the France international now a potential doubt for the 2018 FIFA World Cup as a result.
Although the Gunners responded with commendable spirit, they failed to capitalise on their time in the ascendancy and Atletico showed them how it was done just before the interval, familiar foe Costa netting a fourth goal in seven games against Arsenal.
While Atletico continued to craft chances in the second half, there was a hint of tension in the stands, from where the banned Simeone watched on, that was transferred to the players and gave Arsenal encouragement.
The visitor, still facing a battle just to claim a top-six spot in the Premier League, was simply incapable of breaking through Atletico's exceptionally well-drilled defence as the home side dug deep to hold off Arsenal's late onslaught, booking passage to the final in Lyon on 17 May (AEST).
Atletico – which claimed a late draw in London despite having Sime Vrsaljko dismissed and Simeone sent from the touchline – showed its game-plan right from the start as it set up to counter, using the strength and pace of Costa and first-leg scorer Antoine Griezmann.
That approach nearly paid off after just five minutes – Costa barging his way beyond Nacho Monreal before shooting narrowly wide from a good position in the area.
Arsenal's task was made all the harder when captain Koscielny was carried off with a potentially serious injury in the 12th minute, the 32 year-old evidently in pain.
Yet, Wenger's side actually improved initially after that blow and Alexandre Lacazette – scorer of the tie's first goal – should have put them ahead just prior to the half-hour mark, but he could not get the ball out of his feet after being fed into a glorious position by Aaron Ramsey.
The host, which wasted decent chances through Koke and Griezmann, eventually punished its opponent just before half-time – Costa holding off Hector Bellerin and finishing past David Ospina inside the area following a swift break.
Arsenal stepped things up after the break and nearly levelled early in the second half, but Ramsey scuffed wide under pressure from three defenders after Jack Wilshere's shot ricocheted into his path.
Simeone's side almost took advantage with its next attack as Costa charged into the right side of the area before being denied by substitute Calum Chambers as he was about to pull the trigger.
Despite Arsenal's improvement, it continued to look unimpressive at the back and should have conceded again 23 minutes from time, but Griezmann's close-range effort was blocked following a fine Costa run and cutback.
Arsenal huffed and puffed in the final stages, but its attacks often lacked craft and direction as Atletico clung on to secure a third appearance in the competition's final in the past nine years, leaving Wenger to face up to the fact that his final game of a long and distinguished tenure will now come at Huddersfield Town in the Premier League.