Former India opener Raman was appointed in December last year in rather controversial circumstances by an ad-hoc panel comprising former cricketers Kapil Dev, Anshuman Gaekwad and Shantha Rangaswamy.
Chasing a target of 112, England managed to reach the target with five balls to spare.
Mandhana said she doesn't regret electing to bowl first in the first match, despite the bowlers giving away too many runs.
India lost all their T20s in New Zealand after winning the ODI series and things seem to be heading in a similar direction against England.
The player won the cricketer of the year award for Women at ICC awards and she has said that it had a huge impact on her.
India struggled to 119 for six after Tammy Beaumont (62 off 57) and skipper Heather Knight (40 off 20) steered England to 160 for four in 20 overs.
Notably, Harmanpreet Kaur was earlier the youngest to lead the women's T20I side at 23 years and 237 days before Mandhana took charge.
India have been doing well in the 50-over format but they have plenty to ponder about in the shortest form, having lost their previous series in New Zealand 0-3.
Mithali rued the missed opportunity to not only complete a 3-0 series whitewash against a quality side like England, but also lose out on crucial two points in the ICC Women's Championship.
Chasing India's total of 205/8, England were struggling at 49/5 before all-rounder Danielle Wyatt stitched two crucial partnerships with skipper Heather Knight and Georgia Elwiss to pave the way for their victory.
India outclassed world champions England by 66 runs in the series opener on Friday.
After a mini-collapse, the innings was resurrected by a 54-run stand between Mithali (44) and wicketkeeper Tania (25) for the sixth wicket.
The 33-year-old left arm spinner from Uttar Pradesh, who finished with fine figures of four for 25 against the current world champions, also credited newly-appointed coach WV Raman, for her success.
Batting first, India folded for 202 in 49.4 overs but they returned to dismiss England for 136 to make a winning start to the series.
Earlier this year, it was China that recorded the lowest score against in Women's T20 when UAE bowled them out for just 14 runs.
Opener Smriti Mandhana, who amassed 196 runs including a hundred and a 90 in New Zealand, will be a key player with the bat for the Indian women's team.
Bowling all-rounder Harleen Deol, who plays for Himachal Pradesh in the domestic circuit, is set to replace Harmanpreet in the Mithali Raj-led one-day team.
Mandhana recently scored 196 runs in the three-match ODI series against hosts New Zealand, including a 100 and 90.
Mandhana, asked specifically whether the team was too dependent on her, replied that the perception was not correct.
Mandhana returned as the highest run-getter in the T20 series, amassing 180 runs from three games at an average of 60, including two half-centuries.
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