The midfielder was pleased to get two of his side's goals in the 4-0 win.
The Blues put in a highly accomplished performance against struggling Villa, with an excellent first half display setting them up for the comprehensive win.
It was a patient showing from Roberto Martinez’s side, though, as the away side initially sat deep and looked to hit them on the counter.
That tactic didn’t work out well for them, though, as the result shows, and Barkley was delighted that the Toffees showed their quality as the side pursue a vast improvement on last season’s disappointing campaign.
“We showed how good a team we are,” he told BBC Sport.
“We knew from the start that Aston Villa would get men behind the ball but we showed good patience, defended really well and scored four goals from open play.”
The midfielder was also delighted with his own display, saying he is enjoying the best form of his career to date.
Barkley has started the season on fire for the Toffees, with a hatful of goals and assists, and added another two strikes to his collection against Villa.
He has also impressed on the international stage with England, playing in both of their games during the international break and looking solid once more.
And he says he has taken his form from those games into his club football, admitting his delight at bagging two goals in Saturday’s win.
“I have taken my form from the internationals into this game and I’m buzzing with my goals,” he added.
“I’m enjoying the best football of my career and to get two goals was a bonus.”