But the Dutchman is ready to handle any criticism which comes his way in a campaign which has seen him oversee the loss of a six-point lead over Celtic at the winter break to now trailing their Old Firm rivals by six points with just six rounds of fixtures remaining.
Rangers were unable to capitalise on taking a third minute lead through Aaron Ramsey with van Bronckhorst unhappy with his team’s defending as they conceded goals to Tom Rogic and Cameron Carter-Vickers before half-time.
Van Bronckhorst introduced substitutes Fashion Sakala and Scott Arfield midway through the second half in a bid to salvage the situation but Rangers came up short.
“Our start couldn’t have been any better,” said van Bronckhorst. “The team started on the front foot and we scored an early goal, which is what you want.
“But the two goals we gave away were gifts. It cannot happen in any match – not only an Old Firm – but any match. You cannot give the first goal away like that.
“For me it’s unthinkable. But it happened and for the second goal as well we didn’t defend as strongly as we can.
“It was a game we had to win. There are no excuses in football. There are not excuses for Rangers or me as to why we lost today. I don’t want to find excuses, I just want to play as good as we can with the players we have available. That is my job and that is my task.
"It’s easy to talk about subs and why it didn’t happen. You bring in fresh legs. We put Sakala on the wing to get more bodies up front and to play with a lot of pressure up front.
“We created some chances to score. Not really big ones but enough chances to score the equaliser. If you lose, the subs are always bad. If you win, it’s always good.
“I’ve had both moments in this season so far. It’s the task of a coach and also if it doesn’t go well it’s always the blame of the coach. I have tough skin.”