The Welsh outfit have dropped points at home to Crystal Palace and West Bromwich Albion in their last two games to slip closer towards the relegation zone, but ahead of their testing trips to Goodison Park and the Emirates Stadium, Williams believes that his side can earn a change in fortunes.
The 29-year-old is quoted by Wales Online as saying: "We've beaten good teams before on the road and that's the attitude that we've got to go with.
"Since Monks has been here, we've gone to Liverpool and we've gone to Napoli. We haven't won, but if we can continue to show that attitude, I think that we'll pick up points.
"As much as we're disappointed and angry, I think that we have to look positively at the next two."
Swansea have won just once in eight fixtures since Monk replaced Michael Laudrup earlier this year.