With Liverpool having recently slumped to a surprise defeat at home to Aston Villa, Downing is confident that West Ham can inflict further misery on the Merseysiders at Upton Park.
"If we can cut the errors out, I think we've got a really good chance against Liverpool," he told the club's official website. "You saw what Aston Villa did on Saturday - they shut them out and Liverpool didn't really have many chances. That's what you've got to do because if you're sloppy against top teams they'll punish you.
"If we show the same passing and movement that we did on Monday, but cut the errors out, we can play against anyone. We need to get a result at home too."
West Ham welcome Liverpool to Upton Park on Saturday evening.