The 34-year-old suffered a scare after losing consciousness in the closing stages of the Eredivisie clash, leading it to be abandoned.
NEC had been leading the game 2-1 after 91 minutes, with Dost in inspired form after scoring his side's first before assisting the second.
However, he experienced a sudden collapse in added time, with players from both clubs forming a ring around him as he received treatment.
Dost regained consciousness to acknowledge the stricken fans as he was carried off the pitch on a stretcher.
"The AZ-NEC match was stopped in the 90th minute on Sunday evening with the score 1-2. Bas Dost collapsed on the field and was immediately helped by all the emergency services present," NEC said in a statement on their website.
"Dost was carried from the field by the emergency services and taken to hospital."
Now, Dost has delivered the footballing world the positive news it hoped for by revealing that he was on the road to recovery.
"I'm doing well," the 18-cap Netherlands international wrote alongside a picture of himself with his thumb up in hospital.
"The help I received on the field was fantastic. I'm in the hospital now and I feel good. Thanks for all the support."
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AZ were among the accounts to react to the post, saying: "Bas Dost is fortunately conscious. Wishing you a lot of recovery and strength, Bas."
Dost, who has played for Sporting Lisbon and Frankfurt, had looked to have put NEC on track for a famous win over AZ.
His third goal this season would have led the club up to eighth in the table and hand second-placed AZ their first defeat of the season.
It has yet to be confirmed whether the 2-1 result will stand or if the two will organise a replay at a later date.