Vettel and Schumacher were squabbling over ninth place in the closing stages of the inaugural Miami GP, with Haas driver Schumacher closing in on his first-ever points in F1 and Vettel on his way to a second consecutive top 10 finish.
But on lap 53 the two Germans collided in Turn 1 when Schumacher made a half-hearted move while Vettel was turning in, not expecting to find his compatriot on his inside.
The clash came after Schumacher ran wide in the final set of corners defending from Alpine's Esteban Ocon, which had allowed Vettel through.
Vettel retired on the spot due to the contact, while Schumacher had to pit for a new nose and saw his chance to score points in F1 evaporate in the sweltering Miami heat, coming home 15th.
Afterwards, Vettel, who is close to the Schumacher family and acts as a sort of mentor for young Mick, said the incident was "stupid for both of us" as both drivers lost a good result.
"Of course, stupid for both of us. That's what remains," Vettel told Sky. "I'm sorry we're both out [of the points].
"I thought I had the corner and was in front, I didn't expect him. Then when I saw him, it was too late. I'll have to look at it again. But it's bitter for both of us, of course."
Vettel's top 10 finish would have been a just reward for a recovery race which he and teammate Lance Stroll started from the pitlane due to a fuel temperature issue on both Aston Martins.
Still, Vettel feels he "could have done better" at some key moments of the race as he found overtaking harder than expected.
"It was very, very difficult to overtake. I would have thought it would have been easier," he said.
"I was much faster at the start and then lost a bit of momentum, always felt a step too late. Of course, we benefited from the safety car. I think we could have finished at least eighth today."
On the team radio Schumacher said he thought the corner was his, but after the race he mellowed a bit once the adrenalin had worn off.
"I don't really know. It's obviously super difficult to see things in the rear-view mirrors of these cars," he explained. "It was a very unfortunate way to end the race today."
When asked if his move was perhaps a tad optimistic, he said: "I don't know. I tried not to go super deep, tried to leave a bit of room, but clearly it was a bit too tight."
The FIA stewards decided not to take further action after reviewing the incident because they found that while both drivers played a part in the incident, neither was predominantly to blame.
