Van Bronckhorst led his side into the Scottish Premiership clash against Celtic under pressure to take all three points and put Rangers back level with the Bhoys.
Rangers did take the lead against Celtic through Aaron Ramsey, but were pegged back by Tom Rogic, while Cameron Carter-Vickers then scored the winner for the visitors just before half time.
The Gers are now six points behind Celtic and boast an inferior goal difference, leading to Dalziel to insist the league is lost.
He said post match on Clyde 1: “Rangers players, Rangers fans, I think they know it’s over.”
Dalziel expects some Rangers fans to now call for Van Bronckhorst to go, though he will not add his name to the mix.
“I think Celtic fans at the beginning of the season would have been delighted just to be near Rangers.
“They’ve been absolutely brilliant.
“Rangers’ January window was poor.
“Van Bronckhorst for me, I’m not shouting for him to go, but a lot of Rangers supporters will.
“But the European scene seems to be [the positive for Van Bronckhorst].”
Rangers remain in the mix in the Europa League and are next in action in the competition when they face Braga in midweek.
