The Welsh club dominated proceedings in the Round of 32 first leg against Napoli but could only record a 0-0 draw at the Liberty Stadium.
Despite the fact, Williams was delighted with the effort and performance of his side against a quality Naples outfit.
"We're really pleased with the way we played, it tells you a lot that we're disappointed with 0-0," he told ITV1.
"The message was to get on the front foot and play the Swansea way and we had a lot of chances, the performance as a whole was brilliant."
Williams is now expecting a very difficult trip to the Stadio San Paolo for the second leg next week but insisted that the Swans would take a similar approach as they did tonight.
"It's going to be a tough game, we're under no illusions going out there but we'll take a lot of heart from tonight," he added.
"It will be a difficult game playing away but we'll get on the front foot again and see what we can do."
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