The England international capitalised on Tommy Smith's wayward clearing header to put the hosts ahead five minutes into the second half at Anfield on Saturday.
Sturridge's lobbed finish over advancing goalkeeper Jonas Lossl saw him notch his 62nd goal for Liverpool and the 100th overall in his club career, having previously played for Bolton, Chelsea and Manchester City.
"I didn't even think about that, I completely forgot," Sturridge told the club's website.
"I'm grateful to God for blessing me and allowing me to reach that amount of goals.
"Hopefully there will be a lot more to come - there could've been a lot more but you can never look at the past, you look to the future and say hopefully I'll be able to score another 100 before my career is over."
Handed just his fourth Premier League start of the season by manager Klopp, Sturridge made the most of the opportunity to impress before being substituted in the 74th minute.
While the 28-year-old frontman was pleased to contribute to his side's 3-0 victory, he appreciates scoring against Huddersfield will not necessarily lead to an extended run of games in the first XI.
"It's [about] getting that rhythm, that flow. For myself, I feel like I'm best when I'm like that playing regularly," Sturridge said.
"But the manager picks the team and I'll never cause any issues or problems in the camp because he's the boss, I have a lot of respect for him and for his decisions.
"When I go onto the pitch it's important for me to show what I can do.
"It doesn't matter how many minutes you get, you've got to put your best foot forward and show what you can do for the team. I'm grateful for his faith in me today and hopefully I've repaid him with the goal."