Luiz Suarez' 71st-minute equaliser denied the Black Cats victory at the Stadium of Light on a day when the 96 Reds fans who died at Hillsborough 23 years ago were poignantly remembered.
Rodgers said: "They have been terrific. It's been a difficult week, of course, as you can imagine for the city and everything surrounding it.
"Some of the players have been involved in the tragedy in terms of relatives, so it's been a really emotional week.
"But when you sign for Liverpool, that's part of the contract. As a player or manager, you sign an agreement and a contract with the supporters, an emotional one, and that's all part of the journey of Liverpool.
"We wanted to give hope for two reasons: one, for ourselves, because we have shown really good progress over the course of the weeks - we haven't quite got the results, but the performance level at times has been very good.
"And to end the week for the supporters, because it has been very difficult for them.
"It was a good point all round. We will go away from the game really pleased with the performance."