"It's just time, unfortunately," he said when asked in his post-match press conference what the key is to turning Liverpool's home fortunes around.
"I think there is a real bright future here. It is more or less the same players I inherited and I've brought in one or two who have done really well. It's just going to take that wee bit of time."
Rodgers added that the "incredible" support from the fans will help Liverpool gain a winning momentum soon.
"What is fantastic for me and incredible going forward is the real positive reaction from the crowd," he said. "They're showing they are really behind what we're trying to do. Other clubs wouldn't get that support.
"The only way is by working hard and getting results on the field. The supporters are absolutely incredible."
Liverpool are currently 14th in the league table with six points from seven matches.