After QPR drew 1-1 with West Brom on Saturday, Bothroyd, 29, believes that Neil Warnock's men must up their game if they want to come back from Anfield with a result.
"We've got two tough games coming up now and we are going to have to be on top of our game to get anything from Liverpool and Manchester United - but we believe that we can," said Bothroyd to QPR's official website.
"It will be a tough match at Anfield, but any point away from home is a good point. We have to be positive going into the next two games."
"We can't worry too much about the opposition - that's when you do get beat. We've got to approach the next two games without fear and do as well as we possibly can."