The Nigerian international joined the Reds on transfer deadline day earlier this month on a season-long loan deal from Barclays Premier League rivals Chelsea.
Manager Brendan Rodgers included the 22-year-old forward in his starting line-up at the first opportunity and was rewarded with a goal of eviscerating quality and simplicity.
Afterwards, Moses told Liverpoolfc.com: "It's always great to get on the scoresheet. It was a great goal for me.
"They made a mistake in the middle of the park, I took the ball, cut in and watched the 'keeper - I gave him the face and put the ball in the back of the net.
"It was great to put on the red shirt, get back on the pitch again and enjoy my football. That was the most important thing. It was a great game for us today and we're delighted with the result.
"I think it's a fair result. We could have taken all three points but it wasn't an easy game for us. Coming here, we knew that it was going to be a difficult game. A point was a fair result for us so we're delighted with it."
Moses has joined a Liverpool squad stocked to near capacity with attacking options and watched from close quarters as Daniel Sturridge scored in a fourth consecutive Premier League match.
The No.12 was positioned on the left hand side against Swansea and explained why he would be happy to play any role in an attempt to extend the Reds' unbeaten record.
"I've always played on the left hand side but then again, I'll play wherever the manager wants to play me. I'm comfortable playing anywhere up front," he said.
"We all know Daniel is a great player and a goalscorer as well. He's in great form at the moment, scoring goals. And not just Daniel, Coutinho as well - he's a great player.
"Everyone up front is doing pretty well at the moment. We're still unbeaten, so we just want to keep the momentum going and try to keep winning games."