The Welsh club travelled to Stadio San Paolo on Thursday having drawn the first leg of their last-32 tie 0-0 and looked set to progress on away goals, only for late goals from Gonzalo Higuain and Gokhan Inler to seal a 3-1 scoreline.
Monk will now turn his attention to Swansea's Premier League campaign, with his team sat four points clear of the relegation zone with 11 games to play.
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And former club captain Monk feel Swansea's performances against Napoli give them belief to tackle any side they face.
"The boys there, over 180 minutes, were absolutely magnificent," said Monk.
"The application, the desire, everything you want from a football team - I think they gave it.
"The players now believe they can go anywhere in Europe or round the world and compete against the top teams.
"When you go back into your own league there's nothing to fear.
"When you're coming to places like this and giving a very good team a run for their money, I don't see how you can't enjoy it."
Napoli coach Rafael Benitez was delighted with his charges' efforts in what he was certain would be a tricky tie.
"I was convinced Swansea would cause us problems," he told Sky Sport Italia. "I expected a difficult game, but we remained tight and didn't get too stretched out, so we looked for and found the spaces to win the match.
"Swansea had nothing to lose and came to Naples without pressure, whereas it was a different situation for us.
"We tried to pass the ball around, whereas they could just attack us and throw caution to the wind."
Napoli will face Porto next in the round of 16.