Former US PGA champion Kaymer had been out of form before taking on American Steve Stricker in the final-day singles on the Sunday of the biennial team event.
The 27-year-old German lost the only match he played on Friday's opening day and was omitted by captain Jose Maria Olazabal for both sessions on Saturday.
"The night before the singles Olazabal and myself had a very good conversation with Martin," said world number 19 Garcia.
"Then on Sunday I was having breakfast with Martin and I said to him if I had a wish it would be for him to hole the putt which meant Europe kept the Ryder Cup."
Olazabal, Garcia and vice-captain Miguel Angel Jimenez were invited for a special audience with King Juan Carlos I of Spain at the Palace de la Zarzuela in Madrid on Tuesday as the monarch congratulated the trio on Europe's victory.
"This was my second visit to the Palace to see His Majesty and it was a great honour," said Olazabal.
"The fact His Majesty has invited us to his Palace makes the whole thing very special. There are iconic places and this is one of them but the beauty of this is he has received us because of what we as a team have achieved not just the three of us here today."
King Juan Carlos talked to the trio about the team's exploits and also spoke of five-times major champion and former Ryder Cup great Severiano Ballesteros who died in May 2011 at the age of 54 after a long battle with brain cancer.
"He touched my heart when he mentioned Severiano and he said how sad it was to lose him so early," said Olazabal who added that he still wakes up in the night thinking he is in the middle of the Ryder Cup match again.
Jimenez, one of four vice-captains along with Thomas Bjorn, Paul McGinley and Darren Clarke, said Europe's remarkable comeback from 10-6 down to win 14-1/2 - 13-1/2 meant it could justifiably be described as a unique Ryder Cup.
"One of the most impressive things since we have been back is the number of people who do not play golf and they keep telling us they did not move from their sofa as they watched on the television on the Sunday," said Jimenez.
"They were stuck there with glue. Hopefully, this will create more golfing fans and people will talk more about this wonderful sport. This Ryder Cup was like no other."
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