Dean Smith’s men travel to Elland Road on Saturday targeting a response to their disappointing 2-1 home defeat to Leicester.
Villa sit eighth in the table and have been among the Premier League’s surprise packages this season, already beating their points total from the whole of last term.
But full-back Targett claims players want much more. He said: “We are not happy to settle with what we have got.
“The club has ambition of getting back into Europe and we as players want to be part of that.
“It is our job to keep performing on the pitch and get Villa into the European spots. We have done well at bouncing back (this season) but it is so much nicer when you are winning games.”
Target felt Villa paid the price for ‘wasting’ 45 minutes in Sunday’s 2-1 defeat to the Foxes.
Goals from James Maddison and Harvey Barnes put the visitors two goals up and though Bertrand Traore pulled one back, Villa could not find an equaliser.
“They’re a really good team, a top four team for sure,” said Targett. “Yes, there was a bit of encouragement for us, playing so well in the second half and them holding on but it just felt as though we wasted 45 minutes.
“We huffed and puffed in the second half. The first half wasn’t anywhere near good enough. We weren’t aggressive enough. I don’t think anyone made a tackle. They came here and found it very easy.
“The second half we changed that and got higher up the pitch and started to put them under a bit more pressure.”
Targett admitted frustration at the ease with which Leicester were able to take a two-goal lead.
He said: “It was very disappointing, a real kick in the teeth. They weren’t great goals, to be honest. They were silly mistakes we made and we got punished for that.
“It is hard coming from two goals down in the Premier League. We gave it a good go in the second half and created a few chances but it just wasn’t enough.”