Smith will miss three ODIs and two Twenty20 games to return home and prepare for next month's one-day series in South Africa.
Smith played in all three losing Tests against the Sri Lankans and the first two one-day internationals before it was announced he would fly home to rest up.
Clarke, who retired after last year's Ashes defeat in England, expressed his surprise at the decision.
"I would of (sic) liked to have seen the captain play until the series was won and then have a rest," World Cup-winning skipper Clarke said on social media.
Former Test opener Michael Slater echoed Clarke's sentiments, but Lehmann said he had no issue with their comments.
"It's obviously a burden but a great burden captaining your country," Lehmann was quoted as saying in Australian newspapers.
"We just wanted to make sure that he's fresh and ready to go for South Africa and then the big (domestic) summer ahead.
"We planned that for a long time and he took some convincing. But as a coach and a selection panel we're making sure he's fresh and ready to go each and every time he plays for Australia."
"We respect our former captains and former greats who have an opinion," Lehmann told The Daily Telegraph.
"But we think it's the best thing for Steven to get him right and ready to go.
"It's hard work captaining in all three formats. So we're just making sure he gets a small break, and we're only talking an extra week or two."
David Warner will take over the Australia captaincy in Sri Lanka for the rest of the tour.
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