The Welsh club turned in a fine performance at home to Napoli on Thursday, sealing a 0-0 draw in their Europa League last-32 first leg.
Swansea had plenty of chances to win, and dominated large swathes of the game, despite their Italian opponents' loftier reputation.
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Since the former defender took the reins from Michael Laudrup, Swansea have lost just once and Monk hopes their good form can continue on Merseyside.
"It will be a very difficult game, but we will have a go," Monk told reporters. "I said all along that the best bit is when people doubt you.
"Outside of Swansea, I think most people would have doubted we could get a result against Napoli.
"They played their strongest side and I can guarantee a lot of people would have thought they would wipe the floor with us, but we have proven people wrong.
"We could have put in 10 performances like that but people would still doubt we could get a result against Liverpool.
"For a club like us, we have to continually try and prove ourselves. I said to the players that they are top players, who deserve to compete at this level on a regular basis. I have never doubted them and they shouldn't doubt themselves.
"Don't get me wrong, it will be an extremely tough task to go from here to Liverpool, back to Napoli and then to Crystal Palace, but all we can do is do our best.
"We've done so well up to this point, we don't want to slip up now. We will go there to win, we always do. That has to be the mentality."