But the win over City, followed up by a hard-fought 1-0 success over current champions Leicester on Wednesday night, has restored them to winning ways before the north London derby.
Crystal Palace won the game 3-0.
Sanchez, 28, posted a picture of his cut mouth following a separate clash with defender Robert Huth, whose 86th-minute own goal handed victory to the Gunners.
'Every win gives you a little more momentum, ' a relieved Wenger said.
"In the end I think the win rewards the team that took the initiative in the game".
Manchester City, Manchester United, Chelsea and Paris Saint-Germain happen to be connected with moves for the 28-year old, who scored the extra time victor against the former as Arsenal progressed to the FA Cup final on Sunday.
"You could see that we had some heavy legs [from Sunday]".
And after knocking Pep Guardiola's men from the FA Cup on the weekend, Bellerin spoke of how crucial the goal and the result was: "It was really important for us to get the win today".
"Does it keep us in the race for the top four?"
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But Wenger insisted he would not sell him to a rival.
"We play for us", said the Frenchman, whose future at Arsenal remains up in the air. "You want to be as strong as you can be, and not strengthen the other teams", Wenger said.
Foxes left-back Christian Fuchs grew exhausted of this and proceeded to throw the ball as normal regardless of Alexis being in the way.
Fuchs throwing the ball on Sanchez face.
Wenger then added: "I don't think you would sell him to any Premier League club, that is for sure".
"(Sanchez) got the yellow card because he didn't respect the rules.
To make matters worse for Sanchez, Leicester were awarded a free-kick and he was shown a yellow card.
"I think Christian Fuchs should have got a yellow card at the end as well as Sanchez".
Leicester manager Craig Shakespeare also declined to say whether he thought Sanchez had play-acted.