Neville, a former Manchester United and Everton player, was criticised for his lack of emotion and "monotone" style.
In response, Neville told BBC Radio 5 live the TV role was "a lot harder than I thought it was going to be".
Despite the complaints, the BBC said the footballer would continue to play "a key role throughout the tournament".
A spokesperson added Neville - who is currently a coach for Manchester United and has received broadcast training - was "an important, well-respected member of our team".
Neville told sports presenter Mark Chapman he welcomed the feedback on his performance: "In terms of the content I got out, I thought [it] was quite good.
"But the feedback is that I need to show a bit more excitement, so I think you'll see that more on Thursday night in the highlights show.
"I will get better - it was my first live gig and I'm just glad I helped everyone get to sleep back home!"
The England v Italy match attracted an average 11.5 million viewers, peaking at 15.6 million just before half-time making it one of the most watched programmes of the year so far.
Viewers also took to Twitter to criticise Neville, with several joking England physio Gary Lewin - who was stretchered off after injuring his ankle - had "fallen into a coma" listening to him.
Neville responded saying: "1st live co-comm last night - sometimes u have to take the criticism - it will only make me better- thanks for the feedback (ahhahaha)!"
BBC Radio 5 live broadcaster Danny Baker was among his critics but said the BBC should share the blame.
"Phil Neville has acknowledged he wasn't great during England commentary - but what were the BBC doing giving him that game to 'learn his craft'?" he said.
Neville's next World Cup appearance is as a BBC TV studio guest for Monday night's game between Iran and Nigeria.
The complaints come four months after more than 300 people complained over the corporation's quality of commentary during a snowboarding final at the Winter Olympics.
Viewers complained after Aimee Fuller, Ed Leigh and Tim Warwood cheered when a competitor fell, putting the UK athlete in a bronze medal position.
The BBC has received 445 complaints from viewers about Phil Neville's BBC One commentary on England's World Cup match against Italy.