Daniel Sturridge has pledged to become more clinical for the Reds as he works toward 100 per cent fitness.
The striker needed just seven minutes of his debut at Mansfield to claim a first Liverpool goal, showing composure to find the corner after being found in space by Jonjo Shelvey.
Sturridge had several further opportunities to add to his early tally, only to be thwarted by home goalkeeper Alan Marriott - and the 23-year-old is confident such a scenario will soon be a distant memory.
"I am lacking sharpness in front of goal," he explained to the Liverpool Echo.
"I missed a few chances but hopefully once I get my fitness those ones that I missed will go in.
"I was quite tired out there as I haven't been playing or training much over the last few months. But I'm grateful to the boss for giving me nearly 60 minutes.
"I haven't had much training. I've only had three sessions with the lads and then a light session on Saturday before the game.
"It was a great pass from Jonjo - the vision and the weight of the pass for the goal was perfect. He made it quite easy for me to take the shot first time.
"We haven't had much time to work on stuff but we were both on the same wavelength. We get on well on and off the field.
"All the lads have been great with me and they've made it easy for me to settle in over the past few days.
"I want to say thank you to them for making me feel so welcome. I look forward to playing with them for many years to come."
Sturridge, twice an FA Cup winner during his spell at Chelsea, admitted to pre-match nerves on Sunday. But the No.15 ended the afternoon 'delighted'.
He continued: "It was enjoyable. It was good to get to know my teammates and great for fitness. It's the perfect start for me to score on my debut.
"I was quite nervous before the game. It's weird because I don't usually get nervous.
"People will think 'What, you were nervous against Mansfield?' But this is the kind of game where you are kind of expected to score and you have to score.
"I'm delighted with the win. The FA Cup has been kind to me in the last few years and I'm happy to have helped my teammates win the game.
Asked for his opinion on the winning goal at the One Call Stadium, which saw Luis Suarez handball accidentally, Sturridge instead chose to focus on the fact that the Reds are into the next round.
"I didn't have a great view of our second goal from the bench and I haven't seen it again," the striker reflected.
"I didn't see exactly what happened but the goal stood and we're through to the next round - which is what really matters.
"Credit to Mansfield because they came back at us towards the end. It's the FA Cup and against teams in the FA Cup anything can happen.
"You expect us to beat a Conference team but football is not like that. It's full of surprises and we're just delighted to go through."