The left-back, on loan from table-toppers Chelsea, made his seventh top-flight Villa appearance in last week's victory as they ended a run of four league games without a win.
Paul Lambert's men registered four times before the break as they dismantled Norwich at Villa Park - helping them to a comfortable position off 11th - six points clear of the drop.
Despite looking over their shoulder earlier in the campaign, Bertrand claims Villa are now focused on a top-10 finish.
"We're looking at as high as ninth in the Premier League. But we can definitely push for the 10th spot and that, in my opinion, would be a really good finish," he told the club's official website.
"We don't want to set a limit on it in terms of points. We just want to win as many games as we can between now and the end of the season.
"I think the lads have shown people where the bar can be set, especially against Norwich."
Villa will be without Bertrand on Saturday for the visit of parent club Chelsea due to the terms of his loan deal but the 24-year-old is pleased with his progress since moving to Villa Park in January.
"I had my own personal goals to, first off, get that fitness up in the first few games," he continued.
"Then it was about really start pushing on.
"Paul Lambert was one of the main catalysts of me coming to this club, because he is a manager whose teams play the way that I like to play.
"He really encourages you to express yourself on the pitch so it's always a pleasure to play this way."
