The £29million forward scored twice on his Premier League debut as the Foxes beat Burnley 3-0 at the King Power Stadium on Saturday.
It was just his second appearance for the club after joining from Sporting Lisbon on deadline day and Simpson has been impressed by his work ethic.
"He has done well, Riyad (Mahrez) is here and knows him from Algeria but he is integrating in the team really well," Simpson said.
"He works his socks off and that's what we're about
That's why it's been easy for him to slot in.
"It's great for Islam to get his goals for the club and for the fans to show what he can do for us
Everything was perfect."
Simpson, who returned after missing Wednesday's 3-0 Champions League win at Club Brugge with a hamstring injury, also praised the team's recovery after their trip to Belgium.
"It shows to everyone how far we have come," he told LCFC TV
"Credit to the players and staff after all the travelling, recovery and the right type of training
It's about managing us right and the lads who played on Wednesday
We are in good form, it's a learning curve for everyone but it has worked out really well this week."
Burnley could have scored when Steven Defour headed at Ron-Robert Zieler with the score still goalless, but Leicester never looked back after Slimani's opening goal in first-half stoppage time and boss Sean Dyche admitted the Algerian striker was the difference.
"He is a newcomer and he will adapt to it but his goalscoring record is good and that is the reality of the two teams - £30m on one player," Dyche said, after Ben Mee scored an own goal to wrap up the game for Leicester
"I don't know how much Leicester have spent this year, and rightly so
They are the champions and they want to build and go again but it's right to say we're not in that spending league.
"After that they are a good side and they proved that
When you go 2-0 up and you're playing the Premier League champions it's not impossible but it's improbable that you come back from that
"They get a bit more confident and their tails get up."
Source : PA
Source: PA