The hosts took the lead on Merseyside just before half-time when Steven Gerrard turned home a free-kick, before Daniel Sturridge doubled the advantage shortly after the interval.
Sunderland fought back in the latter stages of the match and brought an air of tension to Anfield when Ki Sung-yueng headed home Adam Johnson's corner.
Gus Poyet's side battled for an equaliser but Liverpool remained stoic in defence and Rodgers was pleased with the way his side responded to the challenge as they closed to within a point of leaders Chelsea.
Manchester City are two points further back in third but have two games in hand and Rodgers believes Liverpool remain third favourites, but he is happy to have proved their doubters wrong.
"I think people looked at us and thought we would tail off," said Rodgers, who believes his team have the character to keep fighting.
"For us there is not the expectancy this year when you look at City, the squad they have and the money they've spent and Chelsea as well as they have been dominant over a number of years.
"The pressure will be there but the pressure is for ourselves. We are Liverpool, one of the biggest clubs in the world.
"We want to represent the club and be winners and we are on that path.
"I felt in the second part of this season we would be stronger because of the nature of our game.
"There were long spells that we were very good at that but as I said as the season goes on we will embrace that pressure and enjoy it
"We keep looking ahead of us, that's always the mantra. We have to keep working well and stay calm.
"We are one point behind Chelsea and still have to play them here.
"But seven wins in a row is incredible at this level where teams are so competitive."
Sunderland enjoyed a strong start defensively and kept a clean sheet for the first 40 minutes and Rodgers applauded the persistence of his side.
"We just had to be patient and let our quality show through," he told Sky Sports.
"I thought our work rate and intensity was outstanding and obviously we scored two excellent goals."
Poyet's decision to play a back five, with two holding midfielders, made Sunderland difficult to break down, but Rodgers was delighted to see Liverpool get the opening goal.
"Teams will be like that near the end of the season, especially here at home," he said.
"It's an intimidating block but we just had to find the touches and combinations to work our way through.
"Obviously the first goal is important in any game, but especially here at Anfield."
Gerrard's opener came from a free kick on the edge of the box after Luis Suarez was dragged down by Santiago Vergini but referee Kevin Friend only produced a yellow card, after Wes Brown appeared to be racing back as cover.
"I thought their player should have been sent off," Rodgers claimed.
"We never got the decision there which would have opened up the game even more.
"Sunderland were probably fortunate there but it was a wonderful free-kick and once we get the first goal, our fluency is better from there."
Although Suarez was unable to add to his tally, Sturridge continued his goal-scoring form but Rodgers insists it is all about the team cause.
"I'm more worried about a great Liverpool team to be honest," he said.
"The two boys are both special talents in their own right, they're both prolific.
"The most important thing for me is the team and as long as they're both working for the team and contributing off the ball, hopefully they can go on to become greats."
Rodgers added: "It's a great arena for us to work in here at Liverpool and when the supporters get behind us, like they have done all season, it's a massive part of our success."