Sanchez said he felt the landing gear buckle beneath the plane as it suddenly came back down and slammed into the ground, skidding off the runway at the General Guadalupe Victoria International Airport in Durango. He described the crash as "very violent."
"As you can imagine, it's a pretty frightening moment," he told reporters on a press call Wednesday. "To be honest with you, I thought that was it."
Sanchez, director of the Shrine of Our Lady of Guadalupe in the Chicago suburb of Des Plaines, Illinois, was visiting his parents' home country this past weekend to celebrate his 50th birthday with family and friends, several of whom were also aboard the Mexico City-bound flight on their route back to Chicago. Sanchez said the aircraft burst into flames shortly after coming to a halt in a nearby field.
"Even though it was raining profusely, the plane was still catching fire," he told reporters. "The smoke was unbearable."
It was not immediately clear what caused the plane to catch fire.
Durango State Gov. José Rosas Aispuro Torres told reporters that the aircraft was lifting off when it tried to abort the takeoff due to bad weather, but it was too late. Weather reports showed scattered storms in the area at the time of the incident.
In an on-camera interview with ABC News, Sanchez said he couldn't see anything but rain outside his window at the time the jet took off and had wondered why the pilot didn't postpone the flight due to the poor conditions.
The four crew members scrambled to get all 99 passengers -- 88 adults, nine children and two infants -- off and away from the burning plane after it crashed. But once outside, they struggled to navigate the area's thorny, rocky terrain as rain and hail beat down, Sanchez told reporters.
"The fire began to spread everywhere and the smoke was billowing," he added. "It was pretty dark, it was muddy, there were rocks everywhere."
Eighty-five people were injured in the crash, including two critically, according to Alejandro Cardoza, a spokesman for Durango state's civil protection agency. Everyone who was on board the plane was taken to local hospitals, he added.
Ashley Garcia, 17, of Chicago, was on the plane with her three cousins. Before the plane crashed, Garcia could feel the wind pushing down on the plane and could see the wind moving the wing outside her window, she told ABC News. She felt a sense of dread sitting on the plane so she started recording what she saw.
"The other side of the window, you could see the trees -- the trees were moving really hard. I didn't think we were going to take off," Garcia said. "Then we started taking off and that's when everything happened."
The fire erupted just a few seats in front of Garcia, she said. She waited in the smoke, struggling to breathe, as everyone escaped the plane from the back.
"When we got off the plane, it was still raining really hard and it was really muddy and we were all soaked," she said. "There was a priest and we all just started praying together. ... I was just so thankful I had gotten out."
Aeromexico, the Mexican airline operating the flight, and Embraer, the plane's manufacturer, said in separate statements Tuesday that they were aware of the "accident" in Durango. Embraer also said that it had sent technicians to the crash site and that the aerospace company "stands ready to support the investigating authorities."
Sanchez was among those injured, telling reporters that he sustained multiple fractures in his arm and will need a surgically-implanted metal plate. He remained hospitalized Wednesday.
"I'll become a bionic priest," he joked during the press call.
Still, he called it an "absolute miracle" that everyone survived the terrifying ordeal.
"I have no doubt," Sanchez told reporters. "If the plane was [going] any faster, the plane would have flipped. If the plane were any higher, it would have been very different."
"It's an absolute miracle," he added. "We didn't lose anyone. Thank God."
ABC News' Jeffrey Cook, Joshua Hoyos, Julia Jacobo, Katie Bosland Kastens, Whitley Lloyd, Victor Oquendo, Sasha Pezenik, Kirit Radia, Darren Reynolds, Scott Withers contributed to this report.