The 28-year-old, who was a second-half substitute, scored with his first touch as new signing Xherdan Shaqiri held the ball up well to link up with Sturridge, who put the Reds ahead.
Sturridge was handed the captain’s armband as James Milner made way after the break as he admitted it was ‘a great feeling’.
“It’s a great feeling,” Sturridge said on being handed the captain’s armband in the second-half. “I’ve been here a long time now. It’s the longest I’ve stayed at one team professionally, apart from Man City in my youth days.”
“This has always been my home. Sometimes it’s good to go away and step back, then come back with a fresh mentality and a new mindset and that’s what it was for me, going away.”
“I never wanted to, but I knew I had to so I could get minutes. But I’m back here to give it my all and help us win something. That’s everybody’s aim, that’s what we’re focused on.”
Sturridge was widely expected to depart Anfield this summer, having had an unsuccessful loan spell away to West Brom.
However, the Birmingham-born striker is set to stay at Liverpool this season, having impressed manager Jurgen Klopp.
“I just wanted to work hard through the summer, help the team and be successful. That's what it's all about.
“I’m not getting too excited, but I’ve got a positive mentality. I’m just focusing on improving, that’s it. You can never stop improving. It's a great group of lads, I feel good but I understand it's a long season too. There’s a lot of games.
“I’m looking forward to the future and seeing what I can do to help the team win something.”
Liverpool were awarded a penalty in the second-half as Sturridge and Ojo both stepped up. After a short discussion, Sturridge stepped aside for the youngster to slot the spot kick away.
“You know what it is, I looked over and the gaffer said, ’Go ahead!’, but I thought for Sheyi, it’s good for his confidence. And also, it’s a big stage especially, for younger players,” Sturridge said.
“I’ve played in big arenas before, but for young players it’s good to get the confidence to score here. He wanted to take it as well, so if you want to show your confidence and want to step up then I’m not going to stand in your way.
“I’m not greedy for the goals. It’s about sharing it around and everyone feeling good about themselves and feeling a part of it.”
The Reds now travel back to Melwood to round up their preparations, before going to France for a training camp.
“It’s been a good vibe. I always enjoy it in the States. I come here for my holidays, it’s always good to play here as well,” Sturridge added.
“You can soak up the atmosphere here as a player, because when you come here on holiday you can blend in easily as nobody really knows who you are.
“When you come here and you play, you really understand the atmosphere and the fans here so it’s great.”