Villa face Manchester United at Old Trafford on Sunday.
“This weekend’s game is obviously going to be a very tough test for us,” said Davies. “I actually think it’s made even harder by the fact that United have lost their last two games.
“They will be looking to win to keep Liverpool at arm’s length at the top of the table.
“They have three suspensions to key players – Wayne Rooney, Nemanja Vidic and Paul Scholes – but they’re able to bring in international replacements in all those positions.
“This just shows the depth of their squad.
The centre-half added: “We have to be positive. We certainly can’t feel too sorry for ourselves after the defeat at Anfield. We just have to pick ourselves up for another big game.
“We have to stay positive about our top-four chances too. If we don’t we might as well give up now.
“We have had a bad March, but we have to stay mentally strong and pick up as many wins as possible. We can’t worry what Arsenal or Everton are doing.”