"I went to apologise because I messed up," the Frenchman told reporters at the Austrian Grand Prix on Thursday.
"I killed a big part of my race but I broke his front wing as well and even though they are fighting at the back, they are still trying to do their best so it wasn't very nice of me to turn into him."
Grosjean, who finished 10th in Montreal after starting fifth, was handed a five-second penalty after the race for the incident that happened as he passed the Marussia with 20 laps remaining.
"It was just a failure of concentration," said the Frenchman.
"That corner is a very tricky corner, a chicane with the wall at the exit, and I was just focussing on the apex and didn't even realise I was turning left. When I saw the replay I thought 'that was bad'.
"It's something you learn and try not to do again."
Stevens appreciated the gesture.
"It was good of him because it was just a racing incident that should never have happened. He obviously thought I was more out of the way than I was but I was as far over as I could possibly get," said the Briton.
"It's good that he came over and apologised and I respect him for that a lot and we can move on and forget about it."
Grosjean's apology showed that he was willing to do as he would be done by, having criticised 17-year-old Dutch rookie Max Verstappen for failing to show remorse after the Toro Rosso driver smashed into the back of him in Monaco in May.
The teenager accused Grosjean of 'brake testing' him and said he was not to blame.
"I said it would have been nice for Max to apologise, I didn't say I wanted an apology," said Grosjean. "We are 20 people in the world doing Formula One and I think respect is one of the biggest things in this sport.
"When you do a mistake and you admit and learn from it, that's fine."
(Editing by Tony Jimenez)
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