The France international penned a three-and-a-half year deal in the French capital on Wednesday, with the Magpies believed to have pocketed in the region of £20m for the move.
Writing in his program notes ahead of today's derby with Sunderland, Kinnear said: "Of course it is disappointing that Yohan Cabaye has moved on after two and a half seasons at St James' Park.
"We didn't want to sell him, make no bones about that, but Yohan made it very clear to us that the opportunity of playing Champions League football and being part of the sporting project at PSG was something he wanted.
"On that basis, we felt that if we received an acceptable bid for him, then it was the right decision for the club to do business."
Laurent Blanc's men drew Bundesliga outfit Bayer Leverkusen in the last-16 stage of Europe's elite competition, the first leg of which takes place on February 18.
The 28-year-old made his club debut in the 2-0 win over Bordeaux at Parc de Princes on Friday evening.