The Watford winger has been called up to the national squad for the first time ahead of qualifiers against Belgium and Macedonia.
Scotland's hopes of booking a place at Brazil next summer are long gone and Anya believes he - and the rest of the team - are free to perform without the weight of expectation on their shoulders.
He said: "Unfortunately, we can't qualify so there is no pressure and we should play free-flowing football.
"We are the underdogs and Belgium are the ones with all the pressure.
"It should be an enjoyable game and hopefully we will get a good result at Hampden Park.
"Maybe if there had been a chance of qualifying, I might have been a bit more nervous.
"Now, I feel comfortable. I can go and express myself without the fear of not being successful."
Anya was born in Glasgow and spent seven years in the city before moving to England as a young boy.
Speaking about the moment he learned of his Scotland call-up, he said: "The gaffer, Mr Zola, pulled me aside when I was eating breakfast and said that he had been in touch with Gordon Strachan, who was going to include me in the list for the Belgium and Macedonia games.
"I was chuffed to bits. I had our keeper to the side of me and he gave me a pat on the back and the usual football banter so it was really good."
Craig Bryson, Chris Burke, Kevin Thomson and Lee Wallace have all been added to the squad after the withdrawals of West Brom pair James Morrison and Graham Dorrans, and Hull forward George Boyd.
However, coach Mark McGhee revealed that Scotland's group status meant Strachan resisted the temptation to recall Steven Fletcher after the Sunderland striker made a scoring return to action at the weekend, having been sidelined since March with an ankle problem.
He said: "I asked Gordon could we do that and Gordon considered it and ruled it out, that it was too early. If there was a lot riding on these two games, I think it might be different.
"In fact, I think Steven Fletcher, himself, might have been on the phone to Gordon saying he wants to come and maybe sit on the bench at worst.
"But we all felt, rightly, that he should be given time and that he will recover and get back to form and back to scoring goals again.
"We will take full advantage of Steven Fletcher in coming matches."