Root’s side chased 164 to win the second Test in Galle by six wickets, and with it their fourth successive series.
England are now unbeaten in 10 matches under his captaincy and have won five consecutive Tests overseas for the first time since World War One.
“We’ve still got improvement in all areas,” said man of the series Root.
“We’ve not had the complete performance in either game.
“We are very clear about how we want to play our cricket and we want to strive to reach that and be more consistent. We’re starting to see that progression and it working time and time again.
“There will be different situations to come and it’s about having that desire to improve all the time.”
The series victory in Galle means England have now won six successive Tests in Sri Lanka,
England are scheduled to play 17 Tests in 2021 with a four-match series in India starting on 5 February.
Root says the challenge for his side now is replicating the performances “over and over again”.
“We know we’ve got so far to go still,” said Root, who has now won 23 of his 45 Tests in charge.
“We’ve got a lot of young players that are learning all the time. We’ve got to look at this as a platform and a starting position and not be happy with what we’ve achieved.
“We’re going to have to play at the top of our game to win in India, but we couldn’t be in a better place to go and challenge them and that really excites me, and should excite the rest of the group.”
England were faced with a 37-run deficit after the first innings but bowled Sri Lanka out for 126 in 35.5 overs to set up the win.
Spinners Dom Bess and Jack Leach had figures of 4-49 and 4-59 respectively, while Root took the final two wickets in successive balls.
Left-arm spinner Lasith Embuldeniya took three wickets to leave England 89-4 in their chase, before Dom Sibley and Jos Buttler shared an unbroken 75 to guide England home.
“The most pleasing thing for me was that the spinners took the responsibility and ownership to get us into that position,” said Root.
“I thought the way we handled the chase with such calmness and poise was really outstanding.
“To deal with that kind of pressure, on a surface like that, shows we’ve come a long way. In the past we’d have made that look a lot more difficult.”
The victory also improves England’s chances of reaching the World Test Championship final at Lord’s in June. They remain fourth in the table and need a comprehensive series win in India to finish in the top two spots. (Courtesy BBC)