The 34-year-old Nigeria international was a major part of the squad that reached the Europa League final and won the Scottish Cup last season, playing 37 games across all competitions.
He was an unused sub in Seville as Rangers lost to Eintracht Frankfurt in a penalty shootout but played the full 120 minutes five days later when Hearts were defeated in extra time at Hampden in the Scottish Cup Final.
However his contract was not renewed and he left Ibrox at the end of the season, but has not yet secured a new club.
Both PSV goals came from set pieces as they first took the lead then scored a second-half equaliser to take a draw to the Netherlands.
Rangers legend and the club’s record goal scorer Ally McCoist has now questioned the decision to let Balogun, who has been in attendance at Ibrox for the last two European games as a fan, leave and urged van Bronckhorst to reconsider while he is still available.
Speaking as a pundit on BT Sport, the 59-year-old, who also managed the club between 2011 and 2014, said: “He’s sitting up in the stand watching Rangers and I’m not too sure I’d have been letting him go.
“You look at Souttar’s injuries, and Helander’s injuries.”
McCoist responded: “Do you know something Kenny? Perhaps there is and it’s not with hindsight I say that.
“I was surprised to see him go – I really, really was.
“And I tell you what, we could have done with him tonight because he’s got height, presence and he scores goals in Europe.”