The Wales striker is the only footballer to have scored in each division from the Conference South to the Premier League AND international football.
Morison, 28, has enjoyed a superb month, netting his first goal for Wales against Montenegro before opening his Norwich account against Sunderland.
Ahead of Friday's clash with Switzerland, he said: "The last month caps all the work I've put in. I've scored at every level but I don't want to be known as someone who scored one in the Prem and one at international level.
"For now, I must keep doing the things I'm doing."
Morison started with goals at Northampton before dropping down the leagues to Bishop's Stortford.
Morison added: "Sometimes there are things you do which are still very non-league and it's about getting those habits out."