Van Gaal has battled a reputation for arrogance throughout his career but did not shy away from that label on Monday after watching United come from behind twice to claim a 2-2 draw at West Brom.
The Dutch manager argued he has bridged a 10-point gap "a lot of times" in his coaching career but while Van Gaal is confident his team are still contenders for the title, former United full-back Gary Neville disagrees.
United will host Chelsea on Sunday, before a Manchester derby against the reigning Premier League champions and a trip to Arsenal before the end of November.
"At this moment in time this Man United team isn't good enough to win the league," Neville said on Sky Sports.
"Louis van Gaal asked for three months when he came in and he's reassessed that. It's a tougher job than he imagined and in the next eight games they've got tough opponents.
"At the start of the season after eight games you would have said they would have been on 16 or 17 points. There's been a lot of upheaval. It's been tough for him."
United have 12 points from eight games to sit sixth in the Premier League table, while their upcoming opponents Chelsea have amassed 22 with seven wins and a draw to lead the English top tier.
But Van Gaal has not given up.
"That's possible [catching Chelsea] but it is difficult to say," he said at his post-match media conference.
"But I am arrogant because I have done it a lot of times."
But Neville argued the 63-year-old manager probably was not as arrogant as he has been previously after a tough start to his stint at Old Trafford.
"Coming out of the World Cup he was drunk with praise, but I think it's sobered him up slightly," the pundit said.
"There's a big belief, I think he will get it right. A lot of good players have been signed but there's been so many injuries, particularly in defence.
"There's something there but it's going to take him longer."
