"We got off to a good start, getting the first goal of the game again, which is important," Rodgers told reporters.
"We had other opportunities to be more convincing in the first half on the breakaway but didn't quite finish them and the keeper made a couple of good saves."
Leicester's Youri Tielemans opened the scoring with a long-range strike following a corner in the 24th minute.
Vardy doubled the lead three minutes after the break when he got on the end of a sublime cross from right back Ricardo Pereira.
Huddersfield halved the lead four minutes later when midfielder Aaron Mooy converted a penalty after Caglar Soyuncu brought down Karlan Grant.
James Maddison restored Leicester's two-goal advantage with a free kick in the 79th minute. Goalkeeper Ben Hamer misjudged the trajectory and took a step to his right before realising too late that the shot was headed to his left.
"When they scored the third our heads dropped and it's difficult," Mooy told BBC. "We've had such a tough season and it's just another day when we were not good enough. It's been a really hard week emotionally."
Vardy sealed victory with a penalty when Terence Kongolo fouled him after he had rounded the goalkeeper.
It was his 104th goal for Leicester, going past former England striker Gary Lineker's haul for the club, and his 15th league goal of the season.
"I can take positives, we don't like the result at all," Huddersfield manager Jan Siewert said. "At halftime we were down 1-0 and we changed it and came out and tried everything... and they scored too easily."
The result lifted Leicester to seventh in the standings with 47 points from 33 games, ahead of Wolverhampton Wanderers on goal difference.
(Reporting by Rohith Nair in Bengaluru,; Editing by Ed Osmond)
