Smart, who will be a restricted free agent this summer, was told that Boston might not be able -- or willing -- to afford the $12 million-$14 million a year price tag that he reportedly has been seeking.
"To be honest, I'm worth more than 12-14 million," Smart told ESPN. "Just for the things I do on the court that don't show up on the stat sheet. You don't find guys like that. I always leave everything on the court, every game. Tell me how many other players can say that."
Smart was told many of his teammates defended his 1-for-10 shooting in an excruciating Game 7 loss to the Cleveland Cavaliers on Sunday night by insisting he is the heart of their team.
"That's what people say," Smart said. "I'm not sure if you can put a price on that."
Smart, who also had seven assists and zero turnovers in 30 minutes, shot 32 percent for the series and an abysmal 22 percent from the 3-point line.
"I don't like to make excuses," said Smart, who underwent surgery in March for a torn ligament in his thumb and returned after just six weeks, "but my thumb is killing me. My whole right hand hurts."
The Celtics can make a qualifying offer of nearly $6.1 million to Smart and can match any free-agent offer that is made by another team, but it's unlikely they will do so if the numbers climb too high. Boston discussed an extension with its gritty defensive specialist, team sources said, but the dollar figures were too far apart. The Celtics are resigned that Smart will opt for a bigger payday elsewhere instead of taking a hometown discount.
Smart also could accept Boston's qualifying offer, play in 2018-19 for the $6.1 million, then become an unrestricted free agent the following summer, in 2019-20.
"I'm not really thinking about that right now," Smart said. "I don't know [if they'll pay me]. We'll find out sooner than later."