England slipped to 85-7 against the minnows but eventually won by 15 runs.
"With an inexperienced team like we have at the moment we are going to make mistakes," said Farbrace, who coached Sri Lanka to the T20 title in 2014.
"We believe we can do very well in this tournament but we have got to learn quickly," he told BBC Sport.
England will return to the same Feroz Shah Kotla Stadium in Delhi to face the Sri Lankans, having successfully defended a modest total of 142 there against Afghanistan.
"Sri Lanka will be thinking about how they are going to play on that surface and we have an advantage in that we have played on it," Farbrace insisted.
Asked about his former team, who lost to leaders West Indies in their second match, he added: "They are not flowing with confidence, they have gone through a fair bit of change.
"Graham Ford is back as coach and Angelo Mathews is an outstanding captain. They have some outstanding spinners but have lost a fair bit of experience."
Having won two of their three matches, England are second in Group 1, with two teams progressing to the semi-finals, but have played a game more than South Africa and Sri Lanka.
"We will take a lot of confidence from the fact we bowled really well, that's our best bowling performance," Farbrace said.
"If we can still win while making mistakes that shows we have got really good character in our side."
Assistant coach Paul Farbrace insists England must learn from a scare against Afghanistan for Saturday's World Twenty20 match against Sri Lanka.