Manager Chris Coleman will hold talks on his future afterWales' World Cup dream was destroyed by the Republic of Ireland.
James McClean's 57th-minute strike gave the Republic a 1-0 win in Cardiff and ensured it would be them, and not Wales, who make next month's play-offs.
It was a bitter blow for Wales who had started the evening still chasing an automatic ticket to the finals in Russia next summer, although Serbia's 1-0 victory over Georgia confirmed them as Group D winners.
Coleman stated after Wales had reached the semi-finals of Euro 2016 that the current World Cup campaign would be his last in charge.
But Coleman's stance appears to have softened and he will speak to his Football Association of Wales employers about the future, probably before a planned Cardiff friendly next month.
"There's a chance I can and a chance I won't," Coleman replied when asked if it was possible he could continue in a job he has held since January 2012.
"I can't give an answer right now. It's not just a matter of signing a new contract, the FAW have been great with me.
"I asked them to leave me alone as my contract has been running down and all the questions were getting asked.
"I wanted to concentrate on getting results. There'll be a conversation in due course and my contract is until the summer.
"But right now, I'm thinking about the experience. I'll go back to my family and take a bit of time.
"When the dust settles we'll see where we go."
Wales were without the injured Gareth Bale and were handicapped further when Joe Allen suffered a first-half head injury.
The groggy Allen had to be substituted 10 minutes before half-time after being caught in an Irish sandwich between McClean and David Meyler, and the Stoke midfielder was assessed by medical staff before leaving the Cardiff City Stadium.
"We missed Joe, he's critical to how we play. It affected us when he went off," Coleman said.
"We just came up a bit short, we needed that first goal, but it went to them.
"We got a bit frustrated, started rushing things, and it wasn't quite enough.
"You have to give (Republic manager) Martin O'Neill a huge pat on the back, they had a game plan and it worked, good luck to them."
Wales had won their three previous games to climb into second spot and had not trailed in any qualifier before McClean struck.
But they ran out of ideas after falling behind and Ireland comfortably soaked up home attacks.
"It's a shame for us, a hard one, but we've got no complaints," Coleman said.
"It's another campaign where we've taken it all the way.
"It's done, it hurts, it's hard - we have a dressing room of devastated players and a nation mourning.
"But our players have done brilliantly and we've got to learn from it."