City secured their third Premier League win of the season when Rodrigo smashed in an 88th minute to take us top of the table.
It was a game that we dominated with more than 80% of possession and a total of 30 shots.
The opener finally came from Erling Haaland in the 63rd minute, his seventh attempt on goal and Dias praised his and City’s calmness, particularly after the Blades’ equaliser threatened to steal a point.
“[We showed] a lot of patience - especially to not get frustrated and keep doing what we do best,” the Portuguese defender said.
“We kept playing our game and it’s always a special moment in a season when you’re able to go on and look for a second after a tough moment with us conceding a goal. We got it and it’s very important.
“Erling has scored a lot of goals. It’s his job - he’s used to it. He was as he is supposed to be - he was tranquil and ready for the next [chance].”
Rodrigo’s late strike left Sheffield United without any points from their opening three games since returning to the top division.
But Dias believes that the Blades' performance shows just why the Premier League is so difficult to win and why every victory is so important.
“For the team that wins the Premier League - it’s a build-up of these small wins and small margins, we all know it,” he added.
“We’ve been here, we’ve done it. We all know how important it was [to win].
“It’s never easy to play a Premier League game. We ended up having most control of the game but until we score the goals it never becomes easy - even when we scored the first the game is not finished and it’s never certain.
“A very tough one but we’re very happy we got through, scored the second and got the three points.”
It was the 200th league win of Pep Guardiola’s time in charge and Dias is looking forward to having the boss back on the touchline soon after he missed the trip to Bramall Lane.
“We all know each other very well,” Dias said. “He’s been with us for a long time so obviously we miss him, and we want him back.
“We know exactly what we’re doing and what we have to do. We understand it’s important he recovers in the best way possible.
“He was in contact the whole time. We had a bit of nerves at the end, but we got the three points, and we keep moving forward.”