But the England captain was bemused by the star batsman's "mic-drop" celebration as he scored the winning runs on Tuesday.
England beat India by eight wickets at Root's Headingley home ground to complete a come-from-behind 2-1 series win.
"The composure he's shown, particularly in the last two games, is the Joe Root we know and trust, He's been outstanding even when he's been low on runs — around the group he's been the same guy, hungry for runs, hopefully that continues for the rest of the summer,”said Morgan.
Root's Yorkshire colleagues David Willey and Adil Rashid took three wickets apiece as the tourists were restricted to 256 for eight.
Root (100 not out) and Morgan (88 not out) shared an unbroken third-wicket stand of 186 as England won with 33 balls to spare.
Door not closed on my T20 career, says Root
Test skipper Root hit the winning boundary to reach three figures and end India's run of nine straight bilateral ODI series wins.
It was an impressive display by England, who top the ODI rankings with India second, especially as they had lost by eight wickets in the series opener at Trent Bridge last week.
"We started poorly (but) as the series has gone on we have improved, it is a benefit of playing a bilateral series. You play against the same team over and over again, it can present different challenges — that constant improvement has been brilliant since Trent Bridge,” Morgan said.
"Today I thought it was clinical, right from the get-go."
Root had helped spark the recovery with an unbeaten 113 in an 86-run win in the second ODI at Lord's on Saturday, after being dropped from the final match of the preceding 2-1 Twenty20 series loss to India.
It was a reminder that although he may not be the biggest hitter, there is still a place for Root's stylish, more traditional, approach in the white-ball game, with his 13th hundred putting him ahead of Marcus Trescothick as England's leading ODI century-maker.
Just about the only jarring note of Root's innings was when he dropped his bat deliberately after reaching three figures, a gesture more associated with rock stars and stand-up comedians.
"He caught me off guard completely. He's made a fool of himself!" joked Morgan.
Root was named man-of-the-series but the man-of-the-match award went to county colleague Rashid after the leg-spinner took three wickets for 49 runs in his 10 overs.
India series more important than top ranking, says England skipper Morgan
Rashid claimed the prize scalp of India captain Virat Kohli for 71 with a classic delivery that pitched on leg and turned sharply to hit off stump.
A stunned Kohli was left staring the pitch in disbelief before beginning a slow walk back into the pavilion.
"It's definitely the most satisfying wicket I've taken, Virat Kohli is one of the best players in the world " Rashid said.
Having whitewashed a weakened Australia 5-0 last month, the manner of victory in Tuesday's winner-takes-all clash would have further encouraged England, who will look to win the World Cup for the first time next year as hosts.
"They are obviously favourites because its their home conditions," India paceman Shardul Thakur said.
"England know better how to play cricket here, so other teams have a big challenge to play here."
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