The Old Trafford legend also thought that the win over Arsenal was a more difficult fixture than rivals Manchester City hosting Tottenham.
Scholes was confident Sir Alex Ferguson’s side would be able overhaul their close rivals and was happy with the position his side were in.
“I think we had the tougher game because it is always more difficult to go away, and we've got the three points,” he said to Sky Sports at the Football Writers’ Association dinner last night.
“There's still three months of the season to go and hopefully we'll be in the right place when the time comes.
“Obviously City are going well at the minute but we are only three points behind and funny things can happen towards the end of the season. We just have to make sure we look after ourselves and get the right results.”
Scholes made a shock return from retirement just a couple of weeks ago in the FA Cup third round derby against City, with the news only being announce on the morning of the game.
He has since played in all three of United’s games, starting in the win against Bolton – where he scored the opener – and coming on as a substitute in the others.
There has been much praise for the former England international from team-mates and former players.
Scholes refuses to get carried away and suggested his impact has not had a huge impact on the team.
The 37-year-old also revealed why he thought his return has not been as difficult as many would expect it to be.
“I don't think I've had too big an effect,” he added
“I think you have to adjust mentally It does take a bit of getting used to but the advantage I'd had was that I'd been at the club for the last four or five months doing a bit of coaching.
“I'd obviously seen the lads every day so it wasn't too difficult to settle back in.”