Lambert was signed from Southampton in the close season for around £4 million in a left-field transfer that caught many off guard.
The boyhood Reds supporter made an emotional return to the club he left as a schoolboy, after years of playing in the lower leagues with the likes of Bristol Rovers, Stockport County and Macclesfield Town.
The 32-year-old arrived at Anfield as a fully-fledged England international, who played at the World Cup in Brazil, and Rodgers believes that the striker will prove himself to be a useful addition to a squad that finished runners-up in the Premier League last season.
Lambert has yet to score for the Anfield club after featuring in the club's pre-season tour of the United States as well as Sunday's 4-0 win over Borussia Dortmund in their final warm-up game.
The new forward was expected to play second fiddle to Daniel Sturridge and Luis Suarez, but the Uruguayan's departure, coupled with the Reds' inability to so far to sign another striker to their ranks, means Lambert has pushed forward in the pecking order.
However, Rodgers has tried to play down the responsibility on Lambert's shoulders and said that he had been brought to Anfield for his football ability rather than a misguided sense of romanticism.
He told Sky Sports News: “Don’t put pressure on Rickie Lambert to get goals. Rickie Lambert’s been brought in here to be a very valuable member of our squad, and he’s proven it, all his career.
“He’s got goals whatever level he’s played at. He’s played at international level and he got goals, at Southampton last season, he got goals, so there’s no need for him to be under any pressure.
"He needs to come in at 32 years of age and contribute to the history of this club. He’s a big supporter of this club, but he’s past that now. He’s here to do a job and I trust him to do the job."
Asked if he was planning on bringing in new players before the close of the transfer window on September 1, Rodgers was coy and said that he was looking for players who fit the right mentality of playing for one of the biggest clubs in England.
“We’ll be bringing in the right characters, that’s first and foremost," he added. "We assess the character and the mentality of the player.
"They’re told exactly what the situation is before they come in, so they’re not coming in blind to any situation. They know exactly the philosophy and the style of which we operate, they know I will speak to them and communicate with them and they know the team will change, because it’s about the squad.”
Liverpool have so far spent around £90 million on the likes of Divock Origi, Adam Lallana, Dejan Lovren, Lambert, Emre Can and Javier Manquillo, but the majority of the spending has been offset by the £75 million received for Suarez from Barcelona.
Rodgers is understood to be keen to bring in another striker after Loic Remy's move was cancelled amid fears over the Frenchman's medical results, although a move for Sevilla left-back Alberto Moreno has been widely reported to be concluded this week.
Liverpool begin their new Premier League season with a visit from Lambert's former club Southampton on Sunday.