The Welsh were battling to hold out for a point after an 86th-minute red card for goalkeeper Wayne Hennessey left them with 10 men.
But deep into stoppage time Iran struck twice through Roozbeh Cheshmi and Ramin Rezaeian.
Wales will now have to beat England on Tuesday to stand even the slightest chance of getting out of the group.
"It's gutting, we're gutted, there's no other way to say it," Bale told the BBC.
"We fought to the last seconds but it's difficult to take. But we have to pick ourselves up straight away, it's going to be difficult but we have one game left.
"We will have to see. What can I say? We'll recover and we have to go again."
Hennessey's rush of blood, when he raced out of his goal and wiped out Iran striker Mehdi Taremi, left Wales with an uphill struggle.
Bale added: "I haven't seen so I don't know - but obviously the red card changed the game completely."
Former Wales striker Ian Rush admitted Iran deserved their victory.
"Second half was like a cup game, both teams needed to win it," Rush told the BBC.
"Wales gave it 100 per cent but it was a lack of finishing and second half Iran were the better team."
Ex-Wales defender Ashley Williams added: "Wales gave it everything like they always do.
"We probably didn't create enough and didn't have enough chances on the Iranian goal. I'm gutted for the boys."