The Foxes are now up to ninth in the Premier League standings after Saturday's victory over Burnley at the King Power Stadium.
That success followed on from a 2-1 home win over Tottenham and a draw at West Ham and the early-season struggles that saw Craig Shakespeare removed as manager now seem a thing of the past.
Five wins and five draws has seen the East Midlanders take 20 points but there will be many more on offer before the start of the new year, with trips to Newcastle and Southampton on the horizon.
Claude Puel will then welcome Crystal Palace and Manchester City as the games come thick and fast in the run-up to Christmas.
It has certainly been a positive few weeks for the club and Simpson wants to see it continue to ensure that all the good work does not go to waste.
"We want to keep it going now. It's confidence and momentum, especially in this busy period in December. To get a point at West Ham and then two wins, it's been a good eight days for us," he told the Leiecester website.
"We've got two away games coming up and they'll be two tough games. It'll be important to have a few days off now, because I think after that, games are every three or four days.
"This is our week to get ready for that run of games and hopefully we can keep this momentum going, keep pushing up the table and getting those points."