United were far from impressive in their opening day defeat at Aberdeen last week but they bounced back at Tannadice by ending the cinch Premiership champions' 40-league game unbeaten run.
A second-half strike by defender Jamie Robson separated the sides and confirmed Rangers' first defeat in the Premiership since a 1-0 loss to Hamilton at Ibrox in March 2020.
Following his first home league game as United head coach, Courts said: "I don't know if it sets the standard for the whole season but I think it probably gives people a bit of an insight into what we are doing, what we are capable of.
"This is a journey that is going to have highs and lows, like any other football club.
"But I think it is a strong statement of intent in terms of what we want to do and where we want to be."
Around 4,600 United fans were allowed into the game as Covid-19 restrictions were relaxed and Courts was pleased to hear and see their enthusiasm.
He said: "When I heard the reception when the players came out to warm up I was blown away.
"I knew the fans would want to come back and have an impact on the performances on the pitch but to actually have them here so early and be motivational for the players was awesome.
"Our fans have a level of expectancy of performance and style but also endeavour, application and hard work and they more than played their part when players were going down with cramp because I think they recognised the players were giving everything to get the result."
It was Rangers' second successive defeat after losing 2-1 to Malmo in the first leg of their Champions League qualifier in Sweden.
Gers captain James Tavernier knows there will have to be improvement in the return game at Ibrox on Tuesday night if Steven Gerrard's side are to make the play-offs.
He said: "Especially after a result like that you always want a game as quickly as possible.
"We have to use this feeling, channel it in the right way and come out firing on the first whistle on Tuesday night.
"It is a massive game for the boys, the club, the fans so we have to be really at it from the get-go."