The midfielder secured the 2-0 win over Motherwell after Kieran Dowell had fired Philippe Clement’s side into an early lead.
The wind and rain caused havoc for both sets of players but Cantwell says the two quick goals were vital to stretch the unbeaten run under the Belgian boss to 16 games.
Speaking to Rangers TV, he said: “We started really well and we got two goals pretty quickly.
“I think getting them early was crucial as the conditions seemed to get worse as the game went on.
“A few times the ball dropped behind us because of the wind but you have to play the conditions sometimes.
“The important thing is we got the clean sheet, two goals and three points.
“I think the quick goals knocked their belief a little bit and for us, we knew we didn’t have to chase the game.
“It probably wasn’t the prettiest game to watch, we didn’t play our best, but in games like that, with these conditions you to find a way to win and we did.”
The midfielder notched his first league strike of the season and his second of the campaign in the win.
Cantwell was delighted to fire his shot low past former Gers keeper Liam Kelly on 16 minutes.
He insists he doesn’t put pressure on himself to net, although he was delighted team-mate Abdallah Sima opted to set him up instead of going for goal himself.
He added: “I back myself in those areas to get goals and I have am glad Abdallah didn’t swing his foot at it.
“I practice a lot in those types of positions to get chances and it was nice to take one.
“The manager knows what type of player I am and how I can benefit the game. Goals and assists are something that comes with my position.
“Goals are nice but I don’t put pressure on myself to get goals.
“I think we showed resilience and character but today was a tough watch and we know that, but we are looking forward to getting back to Ibrox on Wednesday.”