The Reds took a two-goal lead at Anfield in Wednesday’s match thanks to Steven Gerrard’s free-kick shortly before half-time and Daniel Sturridge’s deflected curling effort moments after the interval.
Liverpool were not at their fluent best, though, and had to endure a tense final 14 minutes after Adam Johnson’s corner was headed home by Ki Sung-yueng from close range.
But Rodgers said that his players will be able to handle the tension of the run-in after they climbed up to second place in the table.
Liverpool are now a point behind leaders Chelsea, having also played 31 games, although Manchester City in third place are two points further back and have two games in hand on those above them.
“We have had a wonderful season. There is still a way to go, but the message is to keep believing,” Rodgers said.
“There were long spells where we were very good. As the season goes on we will embrace the pressure and enjoy it. The pressure will be there, but the pressure is for ourselves.
“We have to keep calm, but it always gets hairy when it gets to 2-1 and it means so much to you.”
Rodgers also claimed that there is not the same expectancy at Liverpool as there is with the two other teams in the title race.
Liverpool have a much smaller squad and have not spent as much on players as their rivals, although the Northern Irishman acknowledged that their recent free-scoring form perhaps added to the tension against Sunderland.
“For us, there is not the expectancy, certainly this year,” he said.
“People looked at us and thought we would tail off. I think we need to reinforce the calmness.
“Manchester City, with the players they have and the money they spent, there would be the expectancy there, and Chelsea likewise.
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“However, there is the whole perception that we are going to get three, four, five goals every game, but we knew we were going to have to be patient.
“Seven wins in a row in the Premier League is a huge credit to the players. I thought we showed great character and deserved the victory. We just have to keep chalking up the wins now.”
Sunderland manager Gus Poyet admitted that his players need to show more of the determination and discipline they displayed at Anfield if they are to avoid relegation from the Premier League.
The Black Cats proved to be stubborn opponents and could even have claimed a point had John O’Shea’s late header from a corner gone in, but instead defeat left them three points adrift of safety.
“The game was set up for a big party for Liverpool — four or five goals and everyone celebrating after half an hour,” Poyet said.
“And as the game went on and on, they couldn’t score and we made it something special. The idea was always to stay in the game, not lose the shape, and believe in the system.
“It was the first time we had played 3-5-2, training four or five days. It is all new, but it shows when you understand the game a certain way, you can put teams under pressure. We need more of that.”
Poyet also urged his players to approach their next game against West Ham United as if they were facing one of the top teams in the league.
“All in all, it was an unexpected performance from Sunderland,” the Uruguayan said.
“We should be doing it every week. We don’t for some reason. Maybe we have to play West Ham like they are Real Madrid or Barcelona.”