The Merseyside club progressed to the fourth round of the FA Cup on Monday by winning 2-1 at AFC Wimbledon on Monday and have lost just one of their last 12 games in all competitions.
Liverpool made life difficult for themselves against the League Two side, though, as Adebayo Akinfenwa raised hopes of an upset when he equalised from close range after Simon Mignolet flapped at a corner.
Rodgers' side have been guilty of switching off on several occasions in 2014-15 and the Northern Irishman knows they can ill-afford to keep making errors as they attempt to recover from a disappointing first half of the season.
He said: "In any game of football, no matter how dominant you are, there's always a period of pressure that you will come under.
"It doesn't matter if you have the ball a lot of the game, you still have to defend at some points in that game and, of course, you have to remain calm.
"I think for us, the single biggest thing has been mistakes. It's not so much structurally, we have a tendency at times to make mistakes and that ultimately has cost us.
"I think that's something that we work hard on and we look to eradicate from the game. From the Crystal Palace game [when Liverpool lost 3-1 in November], we needed to change. We needed to get back our model of work and from that, we've slowly got back to a decent level again.
"There's still a lot of work to do. But part of that is ensuring that we don't give away silly goals. That's something that every coach or manager will tell you is continuous."
Liverpool were held to a goalless draw by Sunderland when the two sides met at Anfield last month, but Rodgers expects Gus Poyet's side to show more ambition at the Stadium of Light.
He added: "They're very difficult to break down, they get a lot of numbers behind the ball. They close the space up and you have to work really hard and well to try to find the gaps to get in.
"It will be slightly different at home. They will be the home team and they will want to go on the offensive a little bit more.
"But they have good players and they have shown over the course of the season so far with a lot of draws that they are hard to break down, but that's our job to go there and look to put in a performance that gets the three points."
Steven Gerrard has scored four goals in his last two games and will be hoping to continue his rich vein of form if Rodgers opts against resting the LA Galaxy-bound Liverpool captain.
Daniel Sturridge (thigh) is due to return from the United States before the weekend as he closes in on his long-awaited return, while Joe Allen (knee) could be back in contention.
Sunderland beat Leeds United 1-0 in the FA Cup last Sunday, but are without a win in three top-flight matches.
Sebastian Coates is ineligible to face his parent club, while Poyet has injury concerns over Lee Cattermole (groin), Jack Rodwell (hamstring) and Anthony Reveillere (calf).
