The debate surrounding Gerrard's role in the side is likely to rumble on after Rodgers left the midfielder on the bench for the first 67 minutes at Anfield.
Having inspired Liverpool to a 3-1 victory over Leicester City in midweek, the 34-year-old's absence coincided with one of Liverpool's least impressive attacking performances of a disappointing campaign.
"I can't have any complaints from the players," Rodgers told the BBC. "They're giving me everything and we can't solely rely on Steven. It can't (always) be up to him."
In consigning his captain to the bench, the Liverpool boss perhaps had one eye on Tuesday's crucial Champions League clash at home to Basel.
Rodgers has spoken at length about needing to manage Gerrard, so he is fresh for the biggest occasions.
He was in no mood to criticise Gerrard's team mates, however, after Saturday's draw ensured they had taken seven points from the last nine, a marked improvement after they lost three straight league games in November.
"I thought the players gave everything and in the second half we looked like we could make breakthrough," Rodgers added.
"Sunderland proved this year that they are a hard team to beat. I can't fault the players. They needed a wee bit of luck and it didn't come.
"If you can't win it's important you don't lose. We've taken seven points from nine this week which is a good return for us."
Liverpool, who have looked short of firepower in the absence of long-term absentee Daniel Sturridge, are ninth in the Premier League with 21 points from 15 games.
They are entering a crucial period of the campaign, with Tuesday's winner-takes-all match against Basel, preceding league games against Manchester United and Arsenal and a League Cup quarter-final at Bournemouth.
(Reporting by Toby Davis; editing by Justin Palmer)
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