After being substituted in the 2-1 defeat at Luton, van la Parra completed a permanent transfer to Serbian side Red Star Belgrade for an undisclosed fee.
The 28-year-old joined Huddersfield from Wolves in March 2016, initially on loan before completing the permanent switch at the end of the season.
He made 101 appearances in all competitions for the club, netting seven times.
Huddersfield Town chairman Phil Hodgkinson commented: “We received the offer for Rajiv during the Luton Town game and both him and his representatives made it very clear that he didn’t want to be a Huddersfield Town player any more.
“The club always has to come first and it’s important that the players in our squad are fully committed to the cause. I want players who want to play for this club and its fantastic supporters; they deserve that.
“The offer meets our valuation and the player gets the move he was pushing for.”
Huddersfield caretaker head coach Mark Hudson blasted referee Andy Davies after his side’s winless start to the season continued.
Karlan Grant had put Town ahead two minutes into the second half at Kenilworth Road but they were pegged back by James Collins’s penalty 10 minutes later.
Andrew Shinnie made it 2-1 after 66 minutes despite midfielder Jonathan Hogg being down with what looked like a head injury, with Davies not blowing to allow the physios on.
Hudson has lost all three of his matches in charge since taking over from the sacked Jan Siewert, with his side sitting second from bottom in the Championship.
He said: “There are decisions that I totally disagree with but there’s no point talking about them or the good bits we saw.
“Some of our leaders weren’t strong enough and until that changes we won’t win games.
“The ref stopped play for a first-half head injury and then he doesn’t for their goal, but we cannot just stop – we have to play to the whistle. We then let them dictate the play for a spell and we’ve got to be stronger. You have to show character.”
Luton Town: Sluga, Bolton, Pearson, Bradley, Bree, Tunnicliffe, Shinnie, Butterfield (Brown 52), Collins, Cornick (Mpanzu 87), LuaLua (Jones 90). Unused substitutes: Lee, Moncur, Galloway, Shea.
Huddersfield Town: Grabara, Hadergjonaj, Schindler, Kongolo, Jaden Brown, Hogg (Mounie 77), Chalobah, Diakhaby, Ahearne-Grant, van La Parra (Kachunga 63), Campbell (Pritchard 58). Unused substitutes: Elphick, Bacuna, Schofield, O’Brien.
Referee: A Davies (Hampshire).