The Scots have not been at the business end of major tournament since the 1998 World Cup in France and they will not be in Brazil next summer.
Their 2014 World Cup qualifier against Croatia next Tuesday night will conclude their latest frustrating attempt and at the age of 27, Mulgrew knows that time could be running out.
Reminded that former team-mate Kenny Miller had recently retired from international football having not graced the finals of a big tournament with Scotland, the Celtic player said: "It would be massive to get to the Euros in 2016.
"We just want to finish on a high and give ourselves confidence going into the next campaign.
"Obviously in my career, I would love to play in a major tournament, a Euros or a World Cup, so I will be doing all I can to get involved in that."
Gordon Strachan's side go into the game on the back of a 2-1 away win over Macedonia and with the knowledge that they beat Croatia 1-0 when the two sides met in Zagreb in June.
Mulgrew is looking to finish the campaign with a double over the Croats.
The former Aberdeen player said: "The last wee while has been pretty good so we want to end the campaign on a high. It would be nice to finish with a good result.
"There was a lot of hard work that night (in Croatia). The manager put his ideas across and the team carried them out very well.
"So we have to look to that performance and that result, and other performances, like the ones against Macedonia and even the ones against Belgium and England, to give us belief in the games to come.
"I'm sure the manager will have a formula and he will have us working on it in the days to come."