The Arsenal manager can now likely afford to fill it with thoughts of the Champions League group stages after goals in the second half from Kieran Gibbs, Aaron Ramsey and Olivier Giroud put his side in a strong position to ease past Fenerbahce.
It was a far cry from the dismay of a defeat by Aston Villa on the opening day of the Barclays Premier League, which resulted in the loss of three points but also of the faith of fans. Wenger was the subject of a terse letter from the London club's supporters' trust - the missive placing an agitated focus on a lack of spending and "obsession" with developing young players rather than adding established talent.
Perhaps there was some irony, then, in the identity of Arsenal's first goalscorer last night. Gibbs has been nurtured through the club's youth system by Wenger and took another step with the opener after 51 minutes - scoring from close range after good work by Theo Walcott and Ramsey.
The Welsh midfielder then doubled the lead 11 minutes later with a low 20-yard shot which evaded the grasp of Volkan Demirel, the Fenerbahce goalkeeper. Giroud then rounded off the first-leg success from the penalty spot after 77 minutes, after Walcott had been brought down.
It seems unlikely - even after that defeat by Villa - that Arsenal will return to the Emirates next week and surrender their lead to the Turks. The London side did not get off completely unharmed, though, with Laurent Koscielny - suspended in the next league game against Fulham - going off in the first half after suffering a facial injury.
Arsenal had arrived in Istanbul without several players due to injury, too, but limited the home side to few openings and silenced the home support early on. Fenerbahce, whose place in the European competition is still subject to a hearing by the Court of Arbitration for Sport after they were banned for alleged match-fixing, were stymied.
By contrast, the English side were lively throughout the evening, starting brightly as Walcott sent a low drive shot towards goal which was blocked by defender Bruno Alves in the fourth minute. Just 20 minutes later and Santi Cazorla, back in the starting line up with Alex Oxlade-Chamberlain facing a long stint on the sidelines, almost found Walcott again. Demirel was alert to the danger, though, clearing with his feet, before Giroud headed the rebound wide.
Walcott and Giroud then combined to set up Ramsey for a shot which the midfielder dragged wide. It was not a seamless performance but you sensed that Arsenal would soon have the tie sewn up.
That feeling remained even after Fenerbahce created their first decent opening came four minutes into the second half, Dirk Kuyt firing over the crossbar after Wilshere had been dispossessed. Two minutes later and the hosts were behind - Gibbs turning a shot into the net from barely four yards out. Ramsey then watched as his shot squirmed into the bottom corner and Giroud made it 3-0.
The Turks responded, but timidly. Moussa Sow shot over for in the 71st minute before former Chelsea midfielder Raul Meireles struck a shot wide minutes later. Substitute Emmanuel Emenike then spurned a chance in the final moments.