The Queen's Park Rangers player made his NI debut in March and scored in his second game against Slovenia.
Washington, a postman just four years ago, followed that up with another goal against Belarus on Saturday.
"The last few months have been a crazy time and I don't think it has sunk in yet. I know I have been fortunate," said the 24-year-old.
"Football can be about being in the right place at the right time, and I have been lucky.
"Maybe in a couple of years I will look back and realise how mad it has all been."
Washington  combined representing non-League St Ives between 2010 and 2012 with a job delivering mail.
Having averaged more than a goal-a-game in his 50 appearances for a club in the ninth tier, he then got his break with Newport who paid £5,000 for him.
The Welsh club were promoted to the Football League in his first season, although Washington barely featured.
He then moved to Peterborough in 2014 and by mid-January of this year, when QPR took him from London Road, Washington had scored 15 goals and aroused the interest of Northern Ireland manager Michael O'Neill.
Washington had only been to the country once before his international bow against Wales in March but he qualified through the grandparent rule.
"It was nice to be accepted so quickly and so readily with Northern Ireland," he added.
"Life doesn't get much better. I'm proud of my achievements and just have to try to enjoy it."
Northern Ireland striker Conor Washington counts himself a lucky man as he prepares to head to Euro 2016.