Rodgers' team now lie in eighth place but the Northern Irishman says the gulf between the two north-west clubs is due to United's superior squad depth.
The former Swansea boss, who is in his first season in the Liverpool hot seat, is confident that he can return the Anfield side to title contention if he is given the means to add to his current group of players.
"We needed goalscorers in the club and I think we've got that now" - Brendan Rodgers
"That's the difference for us, the depth of the squad. Once we close the gap in the squad in the coming transfer windows, I've got great faith in the fact that we'll be able to challenge.
"I've seen enough hope in these opening months that we will do that, and today was another example of that."
Rodgers has been able to add Daniel Sturridge to his ranks in the current transfer window and the England international appeared as a half-time substitute to good effect, pouncing when David de Gea could only parry Steven Gerrard's shot to halve the deficit.
With Fabio Borini also returning from the bench after three months on the sidelines with a broken foot, the 39-year-old is hopeful that the attacking burden on top scorer Luis Suarez will be eased.
"The most important thing is getting in good players and what we've got in these players is that they're all flexible," Rodgers added.
"Borini can play through the middle and also off the side. We've seen Suarez all season playing through the middle, but he's spent a lot of his career playing off the side, likewise with Daniel.
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"So it's about getting good players on the field who can fit into the model and fit into the structure. We needed goalscorers in the club and I think we've got that now."
Rodgers also referenced the FA Cup third round tie against Nottingham Forest in 1990 that is often noted as United's turning point under Sir Alex Ferguson and claimed that a similar milestone may not be too far away for Liverpool.
"This [Manchester United] is a football club that has dominated for many years," Rodgers reflected. "People still talk about the game against Nottingham Forest as a defining moment.
"We've got great hope that that will happen here. It's a long journey for us but we believe we can do it."