The Scots won just three of their 10 matches but did enjoy a strong finish to their qualifying campaign thanks to a 2-0 victory over Croatia at Hampden Park on Tuesday night.
It meant six points out of six against the Croats and Martin feels that Scotland should have collected more than the 11 they managed from 10 games.
The Norwich defender told reporters: "We have been unlucky with a couple of results but we have played well - the performances have been there.
"If the performances are there more often we will get the results. That is what we have got to concentrate on.
"We have got a couple of good friendlies coming up so that is another chance to get together.
"All the time, the squad is getting stronger together. The belief is there in the way we want to play.
"The manager (Gordon Strachan) has instilled that in us. We have got a realistic set of lads with realistic ambitions.
"But we want to play in a major tournament eventually and it is up to us to do it."
As for beating Croatia, Martin added: "A clean sheet is massive. I was disappointed not to get one against Macedonia, they scored late on when I thought we deserved one.
"Two clean sheets against Croatia and two wins are excellent."
Everton's Steven Naismith is also upbeat about Scotland's future and added: "We have taken giant steps forward.
"We are more confident, we are going at teams, we are not sitting in and trying to nick a 1-0 win.
"That's been the biggest change, being a bit more expansive.
"We have got quality midfielders and forward players and we can hurt teams and we have got good athletes as well."