He told BBC Radio 5 live that having a flexible currency was "extremely important" to cope with shocks.
"In the shape of the referendum, we've had exactly one of those shocks," he said, but added the Bank would not intervene to boost the pound's value.
Sterling has fallen nearly 20% against the dollar since the referendum.
On Monday it was trading at below $1.22 and â‚¬1.11, having fallen more than 5% in October on concerns about the economic impact of the UK leaving the European Union.
Investors also continued to sell off UK government bonds - sending the yield to 1.2%, the highest level since the Brexit vote - partly because of the weaker pound.
Mr Broadbent, one of three deputy governors at the Bank, said: "Having a flexible currency is an extremely important thing especially in an environment when your economy faces a shock that is different to your trading partners".
Allowing the pound to react "is a very important shock absorber".
Bank governor Mark Carney said on Friday that sterling's weakness would lead to higher prices, a finding that has since been underlined in a report from the EY Item Club think tank.
The latest inflation figures will be released on Tuesday, with economists expecting prices to have risen 0.9% in the year to September.
Mr Broadbent said it was "likely" that inflation would rise above the Bank's 2% target in the next couple of years.
Tesco's dispute with Unilever last week over the rising price of Marmite illustrates how a weak pound could push up inflation, he said.
Mr Broadbent, a Marmite fan who said he "loves" the stuff, said the rising cost of foreign holidays would also contribute to inflation.
However, he warned that controlling prices with tighter monetary policy could hit growth and jobs.
Raising interest rates to meet the Bank's inflation target could lead to "undesirable consequences" such as lower growth and higher unemployment, he said. It's a "trade off", he added.
The deputy governor spoke to the BBC after a forum with university and A-level students in Derby where he explained what the Bank does.
At the moment "we don't really teach" financial education, he told the BBC.
To help people understand the issues better, schools should teach about debt, the banking system and financial decision-making, he said.
The fall in the value of sterling has acted as an important "shock absorber" for the economy, according to Bank of England deputy governor Ben Broadbent.