The result means Wales will not have any participation at next summer's tournament in Russian Federation and has led to doubts over Chris Coleman's future at the helm, despite the loss being their first at home in the last four years.
"All I can think about right now is the faces of the players in the dressing room and their disappointment", said Coleman, who took over in 2012. They are inconsolable at the moment but they should feel very proud. "When the dust settles we'll see where we go", he added.
Ireland are among the four bottom seeds going into the draw.
As things stand Italy, Denmark, Croatia or one of Portugal/Switzerland stand in the Republic of Ireland's way from appearing at their first World Cup since 2002.
"We are in the playoffs".
Handed a start as manager Martin O'Neill implemented a specific game-plan, Arter was asked to provide energy and impetus in the middle of the field, and he played a significant role in James McClean's victor when he dummied Jeff Hendrick's pull-back to leave the West Brom man with time and space to pull the trigger.
"The impression of our campaign?"
Asked if he feared any team, he replied: "I don't think everybody would want to play us".More news: EU's Tusk hopes for Brexit trade talks by December
"We just came up a bit short tonight", Coleman said. It wasn't plain sailing but, thanks to James McClean's goal, they got there.
"We've played against Italy in a game where we had to win, we've played against Germany where we've had to win, and Wales". We are at our best when people write us off but everyone has a huge desire to win. Despite drawing with them just over a year ago in Turin, Spain showed their true quality and emphatically beat the Italians 3-0 in Madrid last month.
The loss against Ireland was particularly hard to take for Coleman, as it marked the first defeat Wales have suffered in a competitive fixture since they lost 3-0 to Serbia in September 2013 in the qualifiers for the 2014 World Cup.
Wales manager Chris Coleman is undecided on his future following the country's failure to qualify for their first World Cup since 1958 - which remains their only ever showing.
Ireland finished the group as runners-up with 19 points, two ahead of Wales who paid the price for too many draws earlier in the campaign. Croatia had a tough group that also featured Iceland and Turkey.
"The success is not an end in itself but a long journey towards a final destination".
The win means the Republic finish second in Group D behind Serbia, with Wales in third.
For Northern Ireland to take 13 points from their six meaningful matches - discounting the two against San Marino - is pretty impressive.