The Italians, held to a goalless draw at the Liberty Stadium last week by the Swans, brought an end to the best ever run by the Welsh side in a continental competition.
"I'm disappointed but I'm not going to put that on the boys," Monk said
"I could not have asked for any more from my players.
"We had more than enough chances in the 180 minutes but my players should be proud of themselves.
"I thought we dealt very well with the atmosphere.
"They can really hold their heads high and be proud of what we've done.
"I'm gutted for the players, I feel for them
Everything we asked of them, they did it."
Monk felt his side's failure to score in the opening leg hurt their chances of progressing in the tie.
"We knew that we should have come here with the lead," he said
"But nevertheless, we performed well, we had our chances to score goals.
"I think we competed against them for 180 minutes.
"We pushed them until the last minute and that's when you realise what a great team we are."
Monk hailed the performance of Napoli goalkeeper Jose Reina, who made a stunning save from Wilfried Bony's header to prevent Swansea taking a 2-1 lead midway through the second half.
"The keeper was great," he said
"I thought the quality of their goalkeeping in the two legs was what made the difference.
"But Napoli have a great team, they have good players
We give all credit to Napoli.
"They have a great coach and we wish them all the best for the future."
Napoli coach Rafa Benitez felt his side were deserving winners despite being tested by a very strong Swansea.
"We have scored three goals today against a team that has done really well," he said
"We deserved to go through.
"We have to give them credit, they made life difficult for us
They defended well and made us work very hard.
"Swansea played without pressure and when you have less pressure, you make less mistakes.
"But we have to be satisfied to have won against a very difficult rival and we are happy to progress."
Source : PA
Source: PA