The Reds set up a home tie with Arsenal in the fourth round of the competition after putting seven past their League One opposition on Thursday night.
Jones claimed two of those goals with fine curling efforts in the first half and was joined on the scoresheet by Xherdan Shaqiri, Takumi Minamino (two), Marko Grujic and Divock Origi.
Reacting to the result, the No.17 told Liverpoolfc.com: "Coming into a competition like this, I think the underdog can always catch you a bit by surprise. But I thought the boys were 100 per cent at it and I think they showed that today.
"I'm happy [with my goals] but more importantly the boys got the win and we go through to the next round.
"They all count – a goal's a goal to me. I'm happy the boys got the win and we're through to the next round.
"I'm looking forward to [Arsenal] and, again, will give 100 per cent if I'm starting or if I'm coming off the bench. I'll give 100 per cent.
"Every game that I play it's an opportunity for me and the rest of the lads. Every game that I'm called upon, I've always said that I'll give 100 per cent. It's what I try to do.
"I think the performances go and show a glimpse of what I'm capable of doing. But I've still got a lot to learn and I need to be patient and my time will come."
The encounter with Lincoln saw new signings Diogo Jota and Kostas Tsimikas make their Liverpool debuts.
There was also a first senior appearance for 19-year-old Rhys Williams, who has progressed through the club's Academy ranks with Jones.
"I've played all the way through the Academy with him," Jones said of the defender. "Then he's had a loan spell and he's done well.
"He's come in and today he 100 per cent looked like a first-team player. He's been around the squad for years.
"I'm really pleased for Rhys and I hope he gets more time playing because he deserves it.
"But again, as young boys we've got to respect the manager and his staff. We're 100 per cent ready and I'm definitely ready to go again when called upon."