Toronto led 4-1 with 11 minutes remaining in Game 7 on Monday, but watched as the Bruins relentlessly chipped away at the lead, scoring twice with their goalie on the bench and once in overtime to stun the visiting Leafs.
It was a bitter end to Toronto's first playoff appearance in nine seasons, which was the longest active post-season drought in the NHL.
Carlyle said Thursday he told his club: "Time will heal this, but we can never forget it."
Nonis said he was satisfied with the level of desire in the Bruins series after what he called a "deer in the headlights" opening game for a largely inexperienced Toronto group.
For the season in its entirety, the Leafs general manager said the club met, but didn't exceed, internal expectations.
Nonis was promoted from assistant general manager when Brian Burke was surprisingly fired in January just days before the shortened season game.
Burke was responsible for hiring Carlyle, who said he was pleased in his first full season on the job with the team's progress on special teams. He stressed that the club will need to continue to adopt a workmanlike attitude in order to take the next steps in the future.
Nonis gave a cautious endorsement of James Reimer as the No. 1 netminder heading into training camp in September.
"James was very good, and I don't think anyone can point to goaltending as an issue with our team," he said.
However, Nonis said he wouldn't be averse to making any move at forward, defence or goaltending if he felt it would improve the club.
Nonis addressed the case of pending unrestricted free agent centre Tyler Bozak, who tore his triceps muscle during the Boston series.
"If there's a contract that makes sense for us and makes sense for Tyler, we'll sign him," said Nonis, stressing the team would walk away if the price isn't right.
He struck a similar tone regarding Phil Kessel, who will be an unrestricted free agent in July 2014.
"I think this is the best stretch of hockey Phil Kessel's ever played," he said.
With the salary cap slated to go down by nearly $6 million US for clubs next season, Nonis and his management team will have a number of hard decisions to make in the weeks ahead.
The team can buy out a player or two through new compliance rules, without having it count against the cap.
Nonis said off the top of his address that the Leafs were humbled and overwhelmed by the level of fan support, pointing out the incredible television ratings and gathering of thousands at Maple Leaf Square in the downtown core.
"It makes you look forward to getting back this season," he said.