The England bowlers were praised ahead of the series against the Proteas but struggled to take regular wickets against an in-form batting lineup.
Anderson believes that some of the praise may have gone to England's head and that they must improve if they are to regain their number one Test ranking.
"It was a huge wake-up call for this bowing attack," Anderson said. "When you get to number one you can start believing your own hype and your own press. When people say you are a great bowling attack you can start believing that and this is a huge wake-up call in this series.
"We have been truly out-bowled in this series and it shows we have a lot of work to do. Maybe we have got a long way to go."
Anderson has not been included in England's squad for the Twenty20 World Cup.