The match ended in a damp draw after only an hour of play was possible on the fifth and final day due to rain, with Sri Lanka on 287 for three in their second innings, still nine runs shy of New Zealand's mammoth first innings of 578.
Mendis and Mathews had saved their team from defeat on Tuesday when they took advantage of a placid wicket to bat the entire day. It was the first time in more than a decade that a wicket had not fallen on a complete day's play in test cricket.
Williamson said he spoke to senior players to try to come up with an idea to break the partnership on the fourth day but nothing had worked.
"Everything we did yesterday didn't provide too many opportunities," he told reporters on Wednesday after stating with a laugh that he might have changed "everything" if he could replay the fourth day again.
"We sat down and had a number of conversations ... and said 'what's something else we can try?'.
"We tried pretty much all of it."
Mendis finished on 142 not out, while Mathews was on 120, having combined for a record 274-run partnership.
"There wasn't a lot happening," said Williamson.
"We tried a few short balls and changes of tack and tried to build pressure for a period of time to buy a wicket to a certain extent.
"Very rarely do you go a whole day where there's not an opportunity regardless of what you try.
"There might be a run out opportunity or anything, but that's credit to the way the Sri Lankan batsmen played and denied us.
"They were very disciplined, very patient, and weren't looking to bat aggressively which might have given us an opportunity. They played very nicely."
Sri Lanka captain Dinesh Chandimal also acknowledged Mendis and Mathews had saved the game for his side, who were dominated by New Zealand over the first three days.
"It's not an easy task when the opposition leads by more than 300," Chandimal said.
"Angelo and Kusal Mendis have done a really good job and they put up a really good partnership.
"At the same time they played for the team. That's the most important thing. That's the most important thing with the way that those guys played."
(Editing by Peter Rutherford)
