It was announced in March that the 33-year-old South African back-rower would be leaving Warriors this summer to join French second-tier side Brive.
Venter had hoped to extend his two-year stint at the club, and head coach Franco Smith has said he'd liked to have retained the forward.
However, Scottish Rugby is reducing the number of non-Scottish-qualified players affiliated to the country's two pro clubs to provide more opportunities for Scottish-qualified players.
When asked about his reasons for leaving at a press conference on Monday, Venter said: "Oh, tricky question. It's from above and all the stuff going on in Scotland rugby with the foreigners. That's basically one of the main reasons. I love this place and I'd love to stay here, but... leave it there."
Venter admits he was not expecting to be released.
"It's rugby, so there's always something and some challenge to overcome, some injury," he said. "So, yeah, it's bad and I didn't like it, but it's rugby. You don't take anything personally.
"You learn to accept stuff and just be better where you can be better and perform where you can perform and enjoy every moment. I'll enjoy this week and hopefully next week."
Venter says he "respects" Scottish Rugby's change of policy with regard to foreign players.
"I understand that's their plan going forward and I respect it," he said. "I am not Scottish, so it's a privilege to be here and to give back to the club and to the country.
"If they make their plans, they have a will to make Scotland rugby better and I hope they succeed in it."
In Friday's URC quarter-final victory over Stormers Venter scored a try and produced a typically robust display in his final home match for the Warriors.
They now face Leinster in the semi-final at Aviva Stadium on Saturday, and the South African is braced for a formidable task as he bids to prolong his Glasgow career by one more week.
When asked what it would require to win in Dublin, he said: "Twenty-three dogs and 80 minutes of just everyone giving everything.
"They're a class outfit with world-class players and world-class coaching staff. But it's rugby. So if we do our stuff right, then we can do it.
"These games, this is what you play for. Big stakes, big crowd, everyone just ready to give everything."