The vote was prompted by David Moffett, Lewis's predecessor, but only four club representatives were in favour.
Speaking on Good Morning Wales, Lewis said: "Things have to evolve and we will continue to sharpen the saw in the best interests of the game in Wales."
He added the WRU can meet the four regions' "financial ambitions" in the new participation agreement.
Wales' four professional regions - Newport Gwent Dragons, Cardiff Blues, Ospreys and Scarlets - are yet to agree a new deal, with the current one expiring on 30 June.
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Chief executive Lewis said the WRU has put a "very detailed proposal" forward which he feels meets the financial needs of the teams.
"But it has to be the right rugby ingredients and the right rugby ingredients must work for all of Welsh rugby," he added.
Lewis said the key issues include developing and keeping hold of Welsh talent and ensuring an "adequate number" of Welsh players take to the field and are not "flooded" by overseas and third-rate players.
The regions are partly funded via the WRU in an agreement which guarantees a set level of income and covers the release of players for Wales international duties.
Other funding comes via participation in competitions.
Mark Davies, acting chief of Regional Rugby Wales, which represents the four regions, previously claimed a new offer to replace the current contract does not offer enough money to the regions.
New Zealander Moffett had won backing from Wales' four regions and 39 WRU member clubs to call an Extraordinary General Meeting, which was held in Port Talbot on Sunday.
But the board overwhelmingly survived the vote, with 462 opposing the no-confidence motion and 18 abstentions.
Welsh Rugby Union chief Roger Lewis said there must be changes after the board survived a vote of no confidence.