"When I was driving I thought, 'what would Niki do?' So I just kept going," The Guardian quoted Hamilton, who started the race from pole position, as saying.
"I definitely felt like he was with me racing today. It was just incredible to see how much support there has been for Niki from across the world, how much respect and appreciation there is for him. As a driver my goal is to be one day as respected as he was. He left a great example and was a real hero to so many," he added.
Lauda, who died on May 20, had played a key role in bringing Hamilton to Mercedes in 2013 and the two had become close friends.
With Sunday's win, Hamilton strengthened his grip at the top spot of the 2019 driver standings. This was Hamilton's third triumph in Monaco, following his successes in 2008 and 2016.
The Briton also admitted that it was the hardest race he has ever had.
"I think it is the hardest race I have ever had; it is in the top five.
"I appreciate a tough race. As an athlete you always want the toughest battles. I am going to enjoy my evening tonight. I can't wait to call my dad and mum see what they thought of it. I will get a chance tonight to talk to Birgit to let her know how much I appreciate her and her support with Niki over these years," the Mercedes driver added.
Ferrari's German driver Sebastian Vettel came second ahead of Mercedes' Finnish driver Valtteri Bottas after a five-second penalty sent Max Verstappen of the Netherlands (Red Bull) to the fourth spot.
( With inputs from IANS )