It also called on BBC Two to improve its reach and for digital channels to provide better value for money.
BBC chairman Michael Grade said there were "lots of good things" this year, but that the corporation's performance was "not by any means perfect".
"Despite the inevitable pressures from multi-channel television and intense radio competition, BBC reach has held up well," said director general Mark Thompson.
Concerns among MPs over BBC bias to be addressed.
The governors said BBC News had "responded sure-footedly... during 12 months of big-breaking stories and set-piece events".
The governors liked Little Britain, but wanted better BBC One comedy
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It gave particular praise to News 24 for its "sober, sensitive, factual and comprehensive" coverage of the Asian tsunami.
But other aspects of BBC output drew some criticism.
Though Little Britain enjoyed great success, the report supported claims that BBC sitcoms were too focused on middle-class suburbia.
And though arts coverage had increased on BBC Two, the governors believe that "current affairs is proving a challenge for the channel".
'From the heart'
The board said BBC Two must "find ways to improve its reach... without endangering its distinctiveness".
"Our best programmes are the ones that come from the heart," said Mr Thompson, who cited Doctor Who, Blackpool and Auschwitz as examples of shows audiences "remember and treasure".
Spending within the BBC rose £101m over the last year, he said - much of it due to coverage of Euro 2004 and the Athens Olympics.
Mr Grade, meanwhile, said BBC radio "has had a strong year overall" and that Radio 1 and Radio 2 were offering services "distinctive from their commercial rivals".
However, he added that there was "no room for complacency".
Mr Thompson defended "creative" EastEnders despite falling ratings
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Speaking at a press conference on Tuesday, Mr Thompson addressed the board's criticisms of BBC Two by saying the channel was in a "transitional period".
"The governors want it all ways," he said. "They want it to be at the forefront of innovation and risk-taking, but they also want its reach to grow."
He added that the impact of losing The Simpsons to Channel 4 was not yet clear.
Mr Thompson also defended EastEnders, saying the BBC soap - which has suffered a huge decline in viewing figures - was "one of our best creative programmes".
"There are some issues with the programme which we are now grappling with," he said. "We want it to be the best it can be."
In March the government announced plans to abolish the BBC's board of governors and establish a new trust and executive board in its place.