Celtic secured the league trophy for the 10th time in the past eleven seasons thanks to a 1-1 draw with Dundee United at Tannadice on Wednesday night that took them four points clear of their Glasgow rivals with one match remaining.
Rangers, who finished 25 points clear in claiming the title last season to deny Celtic 10-in-a-row, had looked likely to defend their crown having held a six-point advantage at the turn of year.
However, dropped points and successive Old Firm league defeats proved decisive as Ange Postecoglou’s side embarked on a 31-match unbeaten run to overhaul Rangers and reclaim the title in the Australian’s first season in charge.
Van Bronckhorst was happy to acknowledge Celtic merited their success in the hope that his side can finish their own season on a high with both the Europa League and Scottish Cup finals to look forward to next week.
"I think the biggest difference [in the title race] is they [Celtic] have more points," van Bronckhorst told Sky Sports.
"We had a good spell in the league and their winning streak has been long.
"That's why they took over the first place and in the end, if you have so many points you deserve to be champions.
"We have to congratulate them and we make ourselves ready for the big week that comes ahead.
"We have to be ready and bounce back as we start from scratch. We have to fight to get another title."
In another interview with talkSPORT, van Bronckhorst added: "Losing the championship this year, we have to credit to Ange and Celtic for the run they've had this season.
"When you're in first place at the end of the season you deserve to win the championship. Being so successful in Europe is massive for all of us, and we can have a historic week next week.
"If we win a European trophy for the second time in our history, that shows how big achievement that is. It can make it a historic season for us if we win both cups next week."