Jame Vardy gave the Foxes the lead at Bramall Lane, with the Blades' big-money striker Oli McBurnie levelling matters in the second period. However, a stunning goal from Leicester youngster Harvey Barnes saw the East-Midlanders leave the Steel City with victory.
'It was a great win for us'
Rodgers said that he was delighted to see his side finally claim maximum points following consecutive draws at the start of the season.
Talking to LCFC TV, the Northern Irishman said: "It was a great win for us. It’s a tough place to come and they’ve got really good momentum over the last couple of years here, Sheffield United.
“The supporters, having had their first three points last week, it was going to be a tough place for us, but I thought we showed many different aspects to the game today.
“We had to have resilience and we had to defend the box. They put a lot of crosses in. At times, we showed real good quality in the game."
'He's a boy that's got a big future'
The Foxes may not have won the game had it not been for Barnes' brilliant strike in the 70th minute of the game; his blitzing half-volley flying past Dean Henderson in the hosts' goal.
Rodgers saved special praise for the Leicester academy product for his impact after coming off the bench.
He said: "I was, of course, very, very happy. It’s a tough place to come, so knowing that we’ve got quality players and they’re going to keep going, was important.
“To score a goal of that technique and quality having just come into the game, I’m so pleased for him. He’s a boy that’s got a big future here at the Club, and like I say, it was a brilliant goal.”