The 1-1 draw against Norwich, in which they had taken the lead, followed on the back of a 3-0 humbling by West Ham.
In three home games they have scored just twice and earned four points and with four matches without a win in all competitions, Rodgers accepts morale needs a boost.
“We have to build that confidence through training and games. It is just step by step,” he said.
“You have to have courage and bravery to play here. There is a great history but embrace it. You have to play positive football.
“There was a feeling of anxiety when I came in. We made it a fortress. Now we are having to build it again.”
Half-time substitute Danny Ings, who scored his first goal for the club, offered some positivity with a much-needed injection of energy while Alberto Moreno, on his first start of the campaign, was also lively.
The sight of Daniel Sturridge back on the field after five months on the sidelines after a hip operation was another welcome boost.
“He is a way off full fitness. His presence and stature will give us something. It is about building his fitness. There is no pressure on him to do that,” he added.