Herath, 40, thus retired after getting run out in the 86th over.
Rangana Herath ended his distinguished Test career face down in the dirt, needlessly run out going for a second run.
'We played some really good stuff, ' Root said.
"If he is fully fit, then he should come back into the team". 'We can go to Kandy with huge amounts of confidence and look to still improve and get better'.
England picked up three wickets in the first session.
Herath retired from global cricket as one of the most successful Lankan bowlers in Tests after Muttiah Muralitharan who scalped 800 wickets.
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And when Leach trapped Kaushal to make the breakthrough, the wickets started to fall with some regularity, his opening partner gone soon after to Moeen caught and bowled. Sri Lanka management said Chandimal will bat in the second innings but they could lose the services of the captain for the series.
At the close of play, Sri Lanka were 15 without loss with Dimuth Karunaratne on seven and Kaushal Silva on eight after hanging on for seven overs.
England's Ben Stokes, center, celebrates taking the wicket of Sri Lanka's Dhananjaya de Silva during the fourth day of the first test cricket match between Sri Lanka and England in Galle, Sri Lanka, Friday, Nov. 9, 2018.
After the lunch, Kusal Mendis hit Leach for four over his head but attempting a repeat the next ball spooned the ball to Moeen and departed for 46.
Home skipper Dinesh Chandimal, suffering from a groin injury that kept him off the pitch all of Thursday, was bowled by Leach for 11.
The final session began badly for the hosts. He accounted for Niroshan Dickwella with the first ball after tea, Stokes making amends for his earlier drop with a sharp take, then added a soft shot from Mathews (53) to his collection. Angelo Mathews scored his second fifty of the match and Kusal Mendis contributed 45 runs to the cause but the rest of the batting order could not hold up and bundled out for 250 runs. The contributions of offspinner Akila Dananjaya came in for especial scrutiny - Dananjaya got only two wickets in the match, and conceded more than 4.7 runs per over.
England's varied attack, with three quicks and three spinners, applied substantial pressure, with the slightly expensive Adil Rashid the only disappointment so far.