Moreno, a summer signing from Europa League winners Sevilla, was at fault for City's opener in the 3-1 defeat, but capped a fine Liverpool performance with a glorious strike in Sunday’s 3-0 win at Tottenham.
And the 22-year-old is eager for his goal against Spurs, which saw him run 60 yards before firing home across Hugo Lloris, to be the first of many for his new club.
"After making my debut and losing against City I had a point to make," Moreno said on the club's official website.
"When I stole the ball from (Andros) Townsend and saw a way through, all I could think about was getting to their goal and scoring. I didn't care how many metres I had to run.
"I hope it isn't my only one as I hope to dedicate many more to Liverpool's fans.
"If they didn't know me before, they will from now on thanks to my goal against Tottenham."
Moreno is looking forward to playing UEFA Champions League football for the first time in his career and revealed he is excited about locking horns with Real Madrid, who have been drawn in Liverpool’s group.
"Playing in the Champions League is going to be amazing," he added.
""It's all new for me and I'm really looking forward to it.
"Plus, we have Real Madrid at Anfield and I'll be wearing Liverpool's colours. It's going to be a unique experience.
"I saw the trophy at Melwood and I got goose bumps. Hopefully we can win it this year. Hopefully that day will come."