Arsenal tackle a rampant Manchester City side - who won 3-0 at Old Trafford in midweek - on Saturday afternoon following the disappointment of conceding a late own goal in a 2-2 draw against Swansea.
That match had seemed set to draw a line under the 6-0 humiliation at Chelsea which ruined Wenger's 1,000th match in charge, with Arsenal coming from behind to lead with two quick second-half goals.
In his role as a TV pundit, Scholes launched a fierce attack on Arsenal under Wenger, claiming they had "midfield players with no discipline" and adding that "there are no leaders" at the north London club.
Wenger, though, insists his squad - which has been hit by injuries to key men like Theo Walcott, Jack Wilshere and Aaron Ramsey - have what it takes to compete with the best.
"If six points (from the top) is a million miles away, then I don't know what the translation from a mile into a point is," Wenger said on Friday morning.
"Everybody has opinions, people who have managed zero games have opinions and we have to accept that.
"What you live with is what you do on the pitch, and all the rest is only opinions.
"We are in a society where there are thousands of opinions every day, and some go for you and some go against you. You have to live with that."
Wenger added: "We have not given up (on the title), believe me and we can show that on Saturday. It is our attitude that will decide that.
"Champions keep going when everybody else would give up. We have an opportunity to show that we have that mentality."
Former England international Scholes also questioned the development of Wilshere, who had yet to go onto the "next level".
Wenger, though, also rejected those claims.
The Gunners boss said: "You cannot say that, Jack Wilshere is an exceptional player for me who has been handicapped by many injuries.
"Once Jack is back and consistently on the pitch, he will prove everybody wrong about that because he is an exceptional player - and Scholes knows that as well."
Wilshere is currently recovering from a fractured foot suffered when playing for England in a friendly against Denmark at the start of March.
Wenger expects the combative midfielder to complete his recovery in time to play some part in the final matches of the domestic season and also be available for the World Cup.
"Jack Wilshere needs more time. I don't know exactly how long, he works very hard on his rehab and it is a fractured bone so you cannot accelerate that process," Wenger said.
"But yes, for the World Cup certainly (he will be back)."
Beating Manchester City would boost Arsenal's flagging title hopes, and also put some distance back between themselves and fifth-placed Everton, who are six points behind and with a match in hand ahead of their showdown at Goodison Park next weekend.
Wenger said: "It is (a last chance to come back on the leaders), but I believe that we have to keep going despite the past two negative results.
"If people say that Everton can catch us, that means we can catch the teams above us as well because they play against each other.
"It is the next game that is of course very important, and the next game is of massive importance because it is Man City and they fight at the top.
"They are the favourites with Chelsea and Liverpool, but when you play one of the favourites, you have an opportunity to shorten the distance to them."
Wenger insisted Arsenal still have plenty left to play for this season.
"Let's not forget we are in an important race in the Premier League, we are in the semi-final of the FA Cup, so it is at the moment not as doom and gloom as everybody paints the situation," he said.
"We live in a period where every game is a definite judgement forever, but life is movement and life is change - change is part of having disappointments and transforming them into success."
Midfielder Robert Pires was part of Wenger's Invincibles side which won the 2003/2004 Premier League campaign without losing a match.
The former France international feels the current generation could do with 'leaders' on the pitch to help them overcome testing situations.
Pires told the London Evening Standard: "Maybe at this moment, for example, when you go 2-0 down in 10 minutes, you need leadership.
"That is most important. When I played, it was with Tony Adams, Martin Keown, Lee Dixon and David Seaman - you need that leadership. Maybe they miss that, especially at these moments.
"Sometimes football is crazy and strange like last Saturday at Stamford Bridge.
"Leaders change the mentality when you have lost. It is not normal to start like they did at Stamford Bridge or Anfield because it is like a final.
"If you want to win the title, you have to win those games so maybe it is a question of mentality."