Root, viewed as a future national team captain, vented his frustration as he walked off for 88 out of England's 284 for four.
An initial not-out verdict was overturned on the Decision Review System, which detected a faint edge behind on an attempted sweep at Ravindra Jadeja.
The Yorkshireman was convinced at the time he had not hit the ball, but is prepared to defer to the technology available.
He was pacified as well by the runs his team-mates made, principally his third-wicket partner Moeen Ali who struck an unbeaten 120, which put England in position to push for a consolation victory. They have lost the series, and trail India 3-0 with just this match to play.
Root was very honest, but magnanimous too, in his close-of-play press conference.
"I was convinced I didn't hit it," he said.
"Obviously the technology suggests otherwise, but it is bitterly disappointing when you're convinced out there that there's nothing.
"If you look at the wicketkeeper's reaction, he's not interested either.
"I think (India captain Virat) Kohli just went with his gut (instinct to appeal), and it worked out."
Root also kicked a boundary marker as he neared the pavilion, but added: "You probably just have to take it on the chin - I must have got a fine one on it.
"I didn't hear a noise, didn't feel anything on the bat. (But) it could be just one that's bypassed me and is genuinely out."
Either way, he admits he could have left the middle more serenely.
"I probably was a bit childish with my reaction as I walked off.
"But playing international cricket, you're going to be disappointed when you feel you've been hard done by - even if you haven't."
Root's disappointment was magnified as he failed, for the 14th time out of 17, to turn 50 into a hundred at Test level.
"It went upstairs and I went up to Mo and said 'I'll be fine, I've not got anywhere near it'.
"Then you see the spike (on DRS) ... it was more disbelief than anything else, I suppose.
"But you sort of just have to suck it up, and put faith in the rest of the guys. I hope we can make that 500 score and put India under pressure."
Moeen's fifth Test century improved Root's mood, the pair having joined forces at just 21 for two and put on 146.
"I thought the way he played was excellent," Root added.
"When he came out there, having just lost two wickets, the maturity he showed - and he has done throughout this year - was brilliant.
"I think he's taken that added responsibility of batting higher up the order really well on this tour.
"He went through the gears, put their bowlers back under pressure and used his feet superbly.
"It shows how good a player he is. He's becoming a world-class top-order batter."