Lord Hall was appearing before an assembly committee inquiry into the review of the BBC's Charter.
He said a long-term decline in English-language programmes by BBC Wales was the result of challenging financial settlements, not management failure.
Lord Hall said a review of the way different communities were portrayed on UK-wide programming was under way.
He also praised the success of the BBC's drama studios in Cardiff Bay.
Asked how the BBC would address issues about the portrayal of Wales, Lord Hall said he was interested in "the best way of getting the best ideas coming out of Wales" on to the network.
"You're saying, 'because you're the BBC this is something that really should matter to you', and it does.
"I want us to get this right, but also I'm grateful for the appreciation that we've done an awful lot in spend terms, and people terms.
"This is now the issue for us, I think."
Lord Hall confirmed his ambition to introduce a single BBC "service licence" for Wales, to replace existing licences that regulate individual radio, TV and online outlets.
AMs asked whether the cut to S4C's budget as part of the UK government's spending review would affect the relationship between the broadcasters.
S4C receives 90% of its funding (around Â£75m) from the BBC, with around 8% (Â£6.7m) from the UK government.
BBC Cymru Wales director Rhodri Talfan Davies told the committee that S4C's budget was a matter for the broadcaster, the UK government and the BBC Trust.
He added that the BBC and S4C would continue to co-produce programmes, and said it remained "vitally important (that) we look for opportunities to collaborate where possible".
The BBC's director general has been challenged by AMs about the broadcaster's portrayal of Wales.