Mbwana Samatta pulled a goal back for Villa but, despite Bjorn Engels hitting a post with two minutes left, a spirited performance could not stop City.
“Three times in a row is a big success. It’s the consistency, incredible,” Guardiola told Sky Sports.
“It was awesome. We struggled in the first minutes and the last ones. They had two clear chances in the first minutes but we played really well, especially in the second half.
“We’ve won a lot. I tried when we arrive, every game we play we try to win it, every competition we try to win it, and three times in a row, being here and winning is great.”
The holders have now lifted the trophy in five of the last seven seasons, with Liverpool the only other team to win it three years in a row, between 1981 and 1984.
Phil Foden, arguably the most surprising inclusion in the City team, revealed he found out on Saturday that he would be involved and the 19-year-old admitted he needs to shine when given such an opportunity.
“The day before, in training,” he replied when asked when he knew he was starting.
“The manager was working on tactics – I couldn’t wait to play. It was an unbelievable day. I have to say fair play to Aston Villa, they gave us a really good game.
“When I play, every minute counts, so I try and do my best and I’m very proud of my performance today.
“You look at players like Kevin De Bruyne and David Silva, who are great, so when I get into the team I have to make the most of it.”
Villa boss Dean Smith refused to blame the controversial decision to award City a corner ahead of their second goal and said he was proud of his players.
“We all know it wasn’t a corner,” he told beIN Sports. “Unfortunately we didn’t defend the corner well enough – 2-0 against a top team like that is very tough but I thought the lads showed a lot of heart and a lot of quality as well.”
Smith added: “I’m very proud of them, we were playing against one of the top teams in the world.
“We knew we would have to be patient without the ball, they went 2-0 up and it is a mountain to climb against a team of that quality but we nearly climbed that mountain.”
Asked if Villa must now take heart from the display as they battle the drop, he added: “We have to.
“You can’t not look at the results from yesterday and because we weren’t playing we end up in the bottom three.
“We have got a game in hand and if we take the performance from today into our league season then we will be OK.”