Paes-Bopanna surrendered the first set in 32 minutes at the Olympic Tennis Centre and the second set in 52 minutes.
It was Paes' record-setting seventh Olympic appearance, which ended on a disappointing note for the veteran player.
Paes-Bopanna converted both break points received but gave away seven break points in the first set. Kubot-Matkowski won three of the seven break points received to win the first set 6-4.
The Indian pair committed 18 unforced errors in comparison to 10 by their opponents in the first set.
The second set was closely contested with both teams retaining their serves to stretch it to a tie-breaker.
But ultimately the Indian pair went down fighting 8-6 in the tie-breaker to bow out in 1 hour 24 minutes.
They won only 59 of the total 132 points played in the match.
Kubot-Matkowski will play the winners of the match between eighth seeded Spanish pair of Roberto Agut Bautista and David Ferrer and Czech Republic's Lukas Rosol and Radek Stepanek in the second round.
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