It leaves the reigning champions fourth in the table, six points behind leaders Arsenal.
"The better team won," said City boss Guardiola.
"Aston Villa were better than us. It was really difficult because they are really physical and able to control many aspects. That is the reason why they are up there, playing good football and we could not do it.
"It's my duty, my job, to find a way to come back because over many years together we were able to find a way to play games, sometimes playing good, sometimes not, but always we found a way to do it -- and now we are struggling."
Guardiola's team have lost all four domestic games this season when the 27-year-old has not been available but he will be back for the trip to Luton Town on Sunday.
"He's important but today we tried with Manu [Manuel Akanji] and John [Stones]," said Guardiola.
"With Rodri we could not win against Liverpool or Spurs. Of course he is important but it's my job to find a way to do it. Today is simple, the better team won. They were better and we have to accept it."
Guardiola said afterwards that Villa, who jumped to third in the table after a 14th straight home win, are now title contenders.
They're only four points off the top and face Arsenal at Villa Park this week but manager Unai Emery is refusing to get carried away.
"Not really, there are seven teams more contenders than us," he said.
"We play against Arsenal and we are going to focus on it. We are happy to be third but to keep it is very, very difficult."