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."

Rees, who starred in BBC drama series Poldark in the 1970s, was 63.
In a statement, her family said they were "deeply saddened" and the actress, who also enjoyed an extensive theatre career, would be "greatly missed".
"Angharad passed away peacefully today with her family at her bedside in London, after a long battle with pancreatic cancer," her family said.
Rees was married to the late Dynasty actor Christopher Cazenove for more than 20 years and they had two sons together, Linford and Rhys, 35.
Linford, the elder of the two, died in a car crash on the M11 in Essex in 1999 aged 25.
In 1994 the actress divorced Cazenove and went on to marry David McAlpine, of the construction family, in 2005, with whom she lived in London.
Rees played Demelza in Poldark, a costume drama based on the novels written by Winston Graham and first broadcast in the UK between 1975 and 1977.
She also had a role in cult classic Jack the Ripper film Hands Of The Ripper and on stage she appeared in A Winter's Tale, Richard II and Romeo And Juliet.
In addition to her acting success, she also founded an eponymously titled jewellery design company based in Knightsbridge, with her pieces featured in the film Elizabeth, The Golden Age.
Her family said she remained an active supporter of the arts and was an honorary fellow of the Royal Welsh College of Music and Drama in Cardiff, the city where she grew up as a young child.
Her funeral will be private but there are plans for a service in celebration of her life which will be announced at a later date.

Martin, 28, has scored seven goals in 17 appearances for Fulham in the Championship this term.
He "made himself unavailable" for Friday's abandoned game at Reading, but Jokanovic insisted he would stay.
"I'm not going to send him back to Derby - he's going to stay with us and respect the contract," said Jokanovic.
"He stopped in training, but I have information from the medical staff that he is available to play. He decided to take a day off."
He continued to BBC Radio London: "We're not a train station, you can't come in and out when you want. We need to respect ourselves, we are the oldest London club.
"I don't know if he will play for Fulham, but I'm sure he's not going to play for Derby."
Earlier this month, Derby manager Steve McClaren said he was surprised Martin was allowed to leave the club under previous boss Nigel Pearson.
Northern Ireland striker Conor Washington counts himself a lucky man as he prepares to head to Euro 2016.
[NEXT_CONCEPT]
Welsh actress Angharad Rees has died after a long battle with cancer, her family has said.
[NEXT_CONCEPT]
Fulham manager Slavisa Jokanovic has dismissed reports that striker Chris Martin could return early to Derby from his season-long loan at Craven Cottage.