Palace hammered the Black Cats 4-1 on Saturday, with all of the goals coming in the second half. In-form striker Glenn Murray and tricky wingers Wilfried Zaha and Yannick Bolasie tore the home team apart on Wearside, with Dann lavishing the trio with praise following the result.
"It's a tough place to come, but I think that the way we played we could have maybe scored a few more goals. I'm delighted with the win and another three points and a great performance," he said.
The first half was a frustrating affair, with both sides struggling to take control and a lot of fouls being given against both teams throughout the opening period. However, Dann admitted that the Eagles were prepared for a "scrappy" encounter and was pleased with how his teammates dealt with the Black Cats.
"It was a bit scrappy and especially with the conditions, it was a bit windy out there, we knew it was going to be that type of game. And with them in a relegation battle, we've obviously pushed on a bit further up the league today [away from them]. We knew what it was going to be like today.
"I think if anyone was going to score in the first half it was probably going to be us, the lads up the top of the pitch were causing their lads trouble," he added.
"I think it showed in the second half when we kept on doing what we were doing and we got the goals that we deserved. That was the message from the manager 'keep doing what you're doing'."
Dann was pleased for goalscorers Murray and Bolasie, with the latter becoming the first Palace player ever to score a hat-trick in the Premier League.
"Glenn was causing some trouble up there, Yannick was running off him and they couldn't deal with them on the day," said the centre-back.
"They managed to get the goals in the second half and they've won the game for us. I'm delighted for Yannick to get his hat-trick, when he's on that type of form he's unplayable.
"Wilf and Glenn [too,] they all played really well today and that's why we scored four goals and could have had more. But, like I said, delighted for Yannick to get the hat-trick.
The 28-year-old stalwart also spoke about how high Palace can move further up the table in the remainder of this season, stating that the new target for the Eagles should be to climb above the teams immediately above them and try to finish as high as possible.
"I think that's the target for the rest of the season [to try and catch the teams above], we've got six or seven games [left] and two home games coming up, so if we keep performing like that we'll just see where we go. We're catching the teams in front of us now, we're not too far away and if we put performances in like that then there's no reason why we can't go past them.
Because the Eagles started the second half so quickly, there were few chances for Dann to get forward himself and get on the scoresheet, which he has managed to do four times in all competitions this season. But, despite his lack of chances, he was pleased for Murray and Bolasie, as well as with the three points that Palace took back to SE25.
"I didn't get a chance to get up there (Sunderland's area) much today," he said.
"We were playing so well in the second half that every free kick and corner was short and I just let the lads up the top of the pitch do what they do well. I love to get on the scoresheet every now and again, but the main thing is the strikers get the goals and do the business for us and they've done that today."