The Dutchman was appointed by Leicester on Friday to replace the sacked Steve Cooper.
Van Nistelrooy left Manchester United after a four-game spell as interim manager following Erik ten Haag's dismissal, having previously served as his compatriot's assistant.
"The third day working at the club, it’s been very busy getting to know everyone," he told reporters after Leicester's first win in six league matches.
"Everybody was involved with that and helping, it was busy and long days but worth it.
"We know the level in the Premier League and we know every game we play that everything has to be right. We have to train and develop our defence, our counter attack, our possession.
"Lots of things to work on but very happy with the three points," the former Manchester United and Real Madrid striker added.
Leicester are 15th in the 20-team table with 13 points from 14 matches. They host fourth-placed Brighton & Hove Albion on Sunday.