European players qualify for their team either via the Ryder Cup World Points List or the Ryder Cup European Points List.
The best four players from the world list automatically qualify, as do the best five players on the European list who have not qualified via the world list, plus three captain's wildcards.
Some critics argue the system prevents the European side being as strong as it could be because too much importance is given to performances on the European Tour - Donald, Casey and Rose all spend large chunks of their seasons playing on the PGA Tour in the United States.
All three players, plus Harrington, chose to play in last week's Barclays FedEx Cup event in New Jersey rather than compete at the Johnnie Walker Championship at Gleneagles and attempt to qualify automatically.
Their decisions led to a lot of criticism, with some questioning their commitment to the European cause, although Casey said his failure to nail down an automatic place was more down the rib injury which kept him out of the game for more than three months last season.
"Being injured last year really hurt my ability to qualify automatically, but I'll be supporting them in the match," said the 33-year-old Englishman, who has played in three Ryder Cups.
"I probably need time to take it in. Simple fact is I'm not on the team. But I think Europe have got an unbelievable team and I wish them the best for the match, simple as that.
EUROPEAN RYDER CUP TEAM
Lee Westwood (Eng) Age 37; Previous Ryder Cups 6
Martin Kaymer (Ger) 25; Debut
Rory McIlroy (NI) 21; Debut
Graeme McDowell (NI) 31; RC 1
Ian Poulter (Eng) 34; RC 2
Ross Fisher (Eng) 29; Debut
Francesco Molinari (Ita) 27; Debut
M A Jimenez (Spa) 46; RC 3
Peter Hanson (Swe) 32; Debut
Padraig Harrington (Ire) 38; RC 5
Luke Donald (Eng) 32; RC 2
Edoardo Molinari (Ita) 29; Debut
"I'm not going to stand here and sort of plead a case for why I should be on the team. It's done and dusted. I tried my hardest and I didn't make it. I wasn't picked. I didn't qualify automatically. I wish I had."
Casey climbed from ninth to eighth in the world with a 12th-place finish on Sunday and also finished 12th in the USPGA Championship three weeks ago.
In addition he finished third in the Open Championship and his match play record - one win at Wentworth and the last two finals in Arizona - is exemplary.
"It's been one of the craziest selections for the Ryder Cup ever when guys in the top 10 in the world [himself and Casey] didn't know they were playing," added Donald, who has since slipped to 11th and who missed the last match after wrist surgery.
Rose said he "only had himself to blame", while outlining a case for why Montgomerie could have picked him.
The 30-year-old lost once on his debut two years ago, winning twice with Ian Poulter and beating Phil Mickelson in singles.
"When you play one you never want to miss another," he said. "I have and I only have myself to blame for that. I'm very disappointed. I figured I had as good a shot as anybody.
"For Paul Casey not to be in as well I think was a very interesting selection. I don't think many people would have got those three [picks].
"Unfortunately two of us were going to be left out, but that's ultimately our own fault. If you put yourself in that precarious position of looking for a wildcard this is what happens.
"I've got a three out of four record and a great ready-made partner in the team [in Poulter]. I thought those sorts of things would be positives in the pros and cons columns, so I'm disappointed not to be able to renew that partnership.
"But you have to pick yourself up and carry on. It's not like I'm Miguel Angel Jimenez trying to do it for the last time either - I've got plenty of time."
Poulter said: "I'm gutted for Justin and Paul - they are two great mates and golfers.
"I know what's going on in their minds. I know what the guys have gone through because I've been there and it's very hard to play golf that way."
This year's Ryder Cup takes place at Celtic Manor in Wales between 1-3 October.
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