Robin van Persie and Danny Welbeck netted in either half to seal a 4-1 win for the champions in David Moyes' first league game in charge.
Wilfried Bony fired a consolation goal home for the Welsh side on his Premier League debut, but it ultimately counted for little.
Van Persie and Welbeck found the net in the first half within the space of three minutes to put United in the ascendancy, and Rangel believes the shock of the quick-fire double was too much to recover from.
"Obviously we're disappointed," he told the club's official website. "We hadn’t lost a game up until now, including pre-season, so sometimes it’s a good thing to have a result like this.
"It was two minutes of madness really - and it ended up changing the game.
"If they hadn’t scored the second goal then I think we would have had a chance in the second half.
"That killed it really, but we gave it everything and we have to accept the defeat and move on.
"It puts things into perspective because we have to get used to losing as well as winning."
Michael Laudrup's side next face Romanian outfit Petrolul Ploiesti for a place in the UEFA Europa League proper, and Rangel is hoping for a good performance to forget their heavy loss to United.
"Thursday’s game will help us forget the defeat, and it is one of those games that we want to win at home," he said.
"I thought we played well today and created lots of chances. But they were clinical and the finishing was the difference in the end."
‘Slot hasn’t come in and changed everything, making it all about himself – it’s been about the players he’s inherited, getting the best out of a system he likes’: Liverpool manager impressing former players with personality and tactical approach
‘We thought we’d signed him, but Chelsea blew us away. I think they signed him so we couldn’t have him, as much as because they really wanted him’: Liverpool actually failed to sign Mohamed Salah in 2014, three years before finally getting the Egyptian
