Craig Levein's side lost 3-1 to runaway Group I winners Spain in Alicante on Tuesday night to miss out on a Euro 2012 play-off spot to Czech Republic.
However, Mulgrew, 25, saw enough in that game, and in Scotland's 1-0 win over Liechtenstein in Vaduz on Saturday to believe the Scots will have a better chance of making the finals of the 2014 World Cup - and he would love to be involved.
"Every player wants to play for their country," said the Celtic defender.
"Watching the game last night and the Liechtenstein game I'm desperate to be involved for my country.
"Craig Levein will do what's right for Scotland and I'll keep trying to play and play well.
"I think Spain is the hardest place to go so it was always going to be a difficult game, not having a lot of the ball.
"But I think Liechtenstein was a good performance and we've got a lot of good players there.
"Scotland are definitely heading in the right direction and I would like to be a part of it."
The former Aberdeen player, who admitted he had not spoken to Levein, denied that he is eligible for selection by the USA.