The Tottenham boss claimed Capello never had any intention of picking West Ham midfielder Parker or Spurs defender Dawson for South Africa and they were only included in the initial 30-man squad to 'make up the numbers'.
He pointed out that both players had memorable seasons for their respective clubs in the Barclays Premier League but were made to feel like 'ghosts' at England's training camp in Austria.
Making up the numbers: Harry Redknapp has slammed Fabio Capello for ignoring Scott Parker despite selecting him in his 30-man squad
The pair played no part in England's recent friendly victories against Mexico and Japan.
And Redknapp, a former West Ham manager, said: 'They tell me Scott trained fantastically every day in training and could not have done any more.
'He worked his socks off. But whatever he did he was not going to go.
Singled out: Like Parker, Michael Dawson was not given a chance to impress
'Someone said to me he felt like a ghost on the trip - like Dawson - they were there but not there and they could sense that.
'The manager didn't really speak to them or give them much feedback. They have not kicked a ball. Dawson and Parker have had great seasons, but you might as well have taken 25 to Austria. They had no intention of them being in the squad and they made up the numbers.'
It is the third time Redknapp has let rip at Capello after he slammed the England manager's tactics following his first game in charge, against Switzerland at Wembley in 2008.
The Tottenham boss has also hit out at Capello's handling of Spurs centre half Ledley King's ongoing knee problems.
Redknapp added to this latest criticism of Capello by expressing shock at Theo Walcott being left out of England's 23-man final squad.
He said: 'I'm surprised, I thought Theo would go. I like him and he has got great ability.
'I gave him his debut and he is inconsistent at times, but he is a winger and flies by people.
'Capello probably had another look at him and was probably frustrated with his final ball against Japan and decided not to take him.
Having a go: Harry Redknapp (L) believes Fabio Capello was wrong to mistreat Parker and Dawson after both enjoyed excellent form for their club this season
'But you only have to look back at Croatia when he scored a hat-trick and ripped them to pieces. He can be a match-winner.
'Aaron Lennon will have days when it doesn't go his way. Theo can come on and give them a problem.'
On Radio 5 Live Redknapp suggested that England midfielder Joe Cole will be leaving Chelsea, saying: 'I've got a feeling he's already agreed a deal with someone and it's not Tottenham.'
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