"We're a side that's getting better at it", Root said.
"Ten, 15 runs more would have been ideal", Tamim said.
If the opener failed to made a better score, the middle players such as Ben Stokes and the captain Morgan will carry the responsibility to score high.
"I think we can expect to see more of what we have been seeing over the past year from South Africa in this tournament - a courageous brand of cricket", concluded the Proteas skipper.
"But our preparation was good apart from this game so we are confident anyway".
"We need more variety in our attack".
Tamim (128) put on 166 runs for the third wicket with Mushfiqur Rahim (79), passing his ninth one-day global hundred from 111 balls as he paced an assault which brought Bangladesh 83 in the last 10 overs - despite the dismissal of both set batsmen to successive Liam Plunkett deliveries.
Spectators have always been advised to get to sporting events early and they could miss the key part of Thursday's Champions Trophy opener between England and Bangladesh at the Oval if they aren't in on time. The other man to stand out was Mushfiqur Rahim.More news: Hillary Clinton blames others, herself for election loss
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Both batsmen, however, fell in successive balls from fast bowler Liam Plunkett to leave Bangladesh 261 for four in the 45th over. Plunkett was the most succcesful bowler for England with 4 for 59.
England have endured plenty of limited-overs anguish in major tournaments over the years but they have a golden opportunity to claim a first ICC Champions Trophy on home soil. Tamim's superlative knock was studded with twelve boundaries and three sixes. To the English, though, this is natural, and expected to such an extent that they remain unfazed. Uncertainty persists as to the condition of Stokes' knee but he - along with Chris Woakes, Moeen Ali and Adil Rashid - will be key to England's chances of success in the Champions Trophy.
Roy, on his Surrey home ground, saw an attempted scoop off Mortaza brilliantly caught by a leaping Mustafizur Rahman at short fine leg.
"You know, 84 obviously doesn't look good", said Bangladesh captain Mashrafe Mortaza.
Root struck his 10th hundred as England gunned down Bangladesh's 305/6.
Through their performances in the last week, Rubel Hossain and Mehedi have, in all likelihood, won individual battles ahead of Taskin Ahmed and Sunzamul Islam for the third seamer and second spinner slots.