There is an argument that the over-celebrations contributed to the side thinking they'd 'made it' and resulted in certain players becoming too confident about their position in the team.
There's also an argument that they didn't - which is far more convincing:
Trescothick lasted another year thereafter, in which time he performed exactly the same as he had all career.
Strauss soon after went into near-terminal decline and has more recently recovered. Said decline owed virtually nothing to his downturn and almost everything to others' ability to work-out his strengths and weaknesses.
Vaughan barely played for the best part of two years thereafter due to injury and performed better than ever after returning.
Bell could hardly have over-celebrated his performances in the series, and his output thereafter improved.
Pietersen has gone from strength to strength since.
Flintoff performed superbly for another year or so thereafter and hasn't played much for the next 3 years due to injury.
Geraint Jones was never that good ITFP and was soon out of the side.
Giles' career was essentially over due to injury shortly after that series.
Hoggard continued to perform well for another couple of years and was then summarily dropped for virtually no good reason.
Simon Jones' career ended with that series.
Harmison, like Geraint, was never that good ITFP, didn't make any real contribution to the series like Bell, and has eventually faded from the scene.
Collingwood was barely a player of note at the time and has since become one.
Tremlett has remained a nearly-man.
Pratt has gone from relative nobody to absolute nobody.
So no real over-celebration there, it's just a nice-sounding thing for which to generalise blame for the failure to kick-on on.