Leading the race on lap 47, changeable conditions forced Hamilton into a spin, the 26-year-old then straightening his McLaren into oncoming traffic.
The manoeuvre forced Di Resta to run wide and off the circuit to avoid colliding with Hamilton, who later incurred a drive-through penalty for his moment of apparent recklessness.
Hamilton, though, later personally said sorry to Di Resta, who finally ended his eight-race points drought with a seventh-placed finish.
"I had a big mistake," said Hamilton.
"My left-front tyre was pretty worn, so I went a bit wide, came out of the chicane and spun which is very, very rare.
"I think it's one of the first times I've spun, and then after that I have to apologise to Paul di Resta. I just didn't see him.
"I had absolutely no clue. I don't know where or what happened, but I got a penalty for something which is to be expected I guess, so I apologise to him."
Di Resta, who criticised Renault's Nick Heidfeld for his lack of an apology after the German ran into the back of him on lap one of last week's race at the Nurburgring, was grateful.
"It was close," said Di Resta on the incident.
"At the same time there are no hard feelings. He said he didn't see me, although was puzzled as to why he got a penalty, even after the race.
"Had he hit me it would have been a disappointing end. If I hadn't taken avoiding action, it would have been a disaster.
"He did apologise, but I can understand why he did it (the move)."
That incident triggered Hamilton's downfall for although reclaiming the lead from team-mate Jenson Button, the eventual winner, a call in switching to a set of intermediate tyres when light rain was falling was a bad one.
Hamilton was forced to switch back to slicks just two laps later, and then served his penalty two laps after that, dropping him to sixth, albeit recovering to take fourth at the flag.
Blaming his radio for the tyre mistake, Hamilton added: "We were having issues. I could hear my engineers but they couldn't hear me.
"It was a very difficult call for them. I heard them say it was going to rain, and it was already spitting, so we opted to go for the wet tyres.
"They called me in and I did the lap, but the tyres went off. It wasn't necessarily the best call, but that's motor racing."
Despite the high of last week's win in Germany, this was another of those low points for Hamilton who is now 88 points adrift of title leader Sebastian Vettel.
"We would have loved a one-two, so I feel like I let the team down a little, but we'll bounce back at the next race," said Hamilton.
For Di Resta, there was obvious relief at finally conjuring a good result as he said: "I was a under a bit of pressure to score points.
"But at the same time I didn't make any mistakes in the last three races that have cost me anything.
"I've always said there would be highs and lows, and I hope we've had a low and are now rebuilding to a high."