But Villa responded defiantly, with Ollie Watkins halving the deficit soon after the restart as the hosts pressed for a route back into the game.
City held on for a sixth successive win in all competitions, and Dias was delighted that he and his teammates were able to weather the storm.
He said: “Definitely (it feels rewarding), especially the way the team reacted after their goal.
“It’s one of those rules that when you come in after the second half try not to concede in the beginning and they ended up scoring a very good goal.
“But the team showed a lot of character in the way we came back.
“If it’s a more controlled game you feel like you’re going to get it but when it’s a tight game the feeling is always extra at the end.
“It feels (like), and it is an important win. Everybody was very engaged, and we showed a lot of our quality.”
Hear Ruben’s post-match thoughts in full via the video above…