The claret and blues opened the season by beating Arsenal at Emirates Stadium before collecting another two victories, including a 3-2 win against Manchester City, on their way to 11 points from their first 10 Premier League fixtures.
However, a goalless stalemate at West Ham last time out left Villa languishing in 14th and Westwood admits the standards must be raised.
Victory in the South Wales derby on Sunday allowed Cardiff to jump above Villa but the 23-year-old insists his side will leapfrog the top-flight newcomers when they meet on Saturday.
"That is the main aim, to win the games at home, but we have played something like the top seven and we have done well," he told the Birmingham Mail.
"We haven't got the credit we deserve and there are teams around us we need to be beating.
"People looking from the outside will think Villa have only picked up so many points but the run we've had we've done really well to get that amount of points.
"You look at the start of the season and we beat Arsenal and then within three days you've got Chelsea and then Liverpool. It's a tough league but that's why it's great to play in this league against the top teams. It's what you strive for."
Villa have taken eight of their 11 points away from home but their home record, excluding the win against City, has been woeful thus far, with losses against Liverpool, Newcastle, Tottenham and Everton.
Westwood believes a point at Upton Park last weekend was valuable but remains adamant Villa are always out to win.
"You look at those fixtures and they are points you should be taking, especially at home," he added.
"Hopefully we can do that. I thought Saturday at West Ham was a great point.
"We go into every game expecting to win, we don't say 'ah, we can get a draw there'. We go to win every game and that's something we always try to do."