Lemar showed Arsenal supporters what they were missing by scoring his first two goals for France in their 4-0 World Cup qualifying win over Holland - the first of which was a sublime volley.
Arsenal made an 11th-hour effort to sign the 21-year-old in a club-record deal, reportedly worth £92 million (A$150 million), but did not have time to get the transfer over the line.
That meant Chilean forward Sanchez was prevented from joining City as Press Association Sport understands Arsenal were only prepared to let him leave if they recruited a big-name replacement.
City had reportedly tabled a bid worth up to £60m (A$98m) but Sanchez will now remain at Arsenal with his contract expiring at the end of the season.
One player who did land a move away was England international Alex Oxlade-Chamberlain, who completed the formalities on his transfer to Liverpool.
The midfielder's move to Anfield was one of the biggest domestic transfers of deadline day as Oxlade-Chamberlain insisted he wants to take his game to the next level.
"The decision to leave was tough after being a part of the club for so many years, but I feel that this move is right for the next stage in my ongoing development," he said.
The deadline-day outgoings continued as forwards Lucas Perez and Joel Campbell completed loan moves away from the club
Perez returned to previous side Deportivo La Coruna for the season while Costa Rica international Campbell signed a similar deal with Real Betis.
Campbell has been on Arsenal's books since 2011 but this is his sixth temporary move away from north London and will be his second spell on loan in Seville.
Defender Calum Chambers was reportedly the target of two big-money bids from Leicester but Arsenal were adamant he would be staying put.
Kieran Gibbs left for West Brom on Wednesday while Cohen Bramall and Carl Jenkinson are currently on loan at Birmingham, although the latter is sidelined having dislocated his shoulder on his Blues debut.
Having missed out on Lemar, Wenger failed to add to the earlier summer signings of Sead Kolasinac and Alexandre Lacazette despite only finishing fifth in the Premier League last season.
Other summer departures included Poland goalkeeper Wojciech Szczesny joining Juventus last month and Valencia signing defender Gabriel earlier in August, while a host of other youngsters were moved on.