Fly-half Barkley, 30, will make his move to Paris at the end of the month, bringing to an end his 11-year association with the Premiership club.
"It was quite a bolt out of the blue," Blofeld told BBC Radio Bristol. "We only became aware of it a few days ago.
"We're very sad to see him go but we weren't going to stand in his way."
Barkley, who has 23 England caps, will join Racing as a 'medical joker' - cover for an injured player - which is the only way French clubs are allowed to acquire new signings at this stage of the season.
"A series of unfortunate events at Racing have opened up that opportunity and he's very keen to take it," continued Blofeld.
"They have lost three fly-halves and they're looking for a kicking fly-half. They thought they could lure him over there and they have."
Blofeld moved quickly to deny suggestions that Barkley's sudden departure was connected to the player's fractured relationship with coach Mike Ford.
The pair were reported to have fallen out during Ford's time as England's defence coach, but it is understood they held clear-the-air talks when Ford was appointed on Gary Gold's coaching team at Bath over the summer.
"There's no clash at all," insisted Blofeld. "They had history in the past but that was all forgotten a long time ago. It's water under the bridge."
“ I leave with a heavy heart to take on what will be a big challenge. Thank you to everyone @bathrugby for a making the last decade one that I will forever see as one that has shaped my life, friendships and memories”
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