The Chelsea striker scored last in the Three Lions' 7-0 romp over Montenegro which booked their place at next summer's tournament.
His maiden goal for his country completes a memorable 2019 for the 22-year-old after winning promotion to the Premier League with Aston Villa and scoring 11 goals in 18 games for Chelsea this season.
With three group games and a possible semi-final and final at Wembley it is effectively a home tournament for England and Abraham has set his sights on an even better 2020.
Asked what next year might hold in store for him, he replied: "Bigger dreams hopefully.
"Being at the Euros, winning it, top four or top two in the Premier League. Just believing! The sky's the limit.
"Hopefully, hopefully, I don't want to jinx myself."
When pushed on whether England can end 54 years of hurt next summer, he said: "I believe so."
Abraham's game has gone to the next level this season, but he thinks he can get even better working alongside Harry Kane when on international duty.
Kane took his tally to 31 goals for England with a clinical hat-trick against Montenegro, taking him above Alan Shearer, Nat Lofthouse and Tom Finney on the all-time list.
Abraham is right at the bottom of those standings, but is keen to learn from the Tottenham striker in order to make a quick rise.
"It's always been a dream for me to be on the same pitch as him," he added. "Every day, I watch him, learn off him.
"To be on the same pitch with him, training with him every day, watching learning off him, it's always nice to have that type of player to learn from.
"It's for me to add to my game. You saw, his great finishing, even in training practising, you can see his professionalism.
"He wants to be the best, to have someone like that to look up to is a dream."
Abraham's rise to prominence this season has not come as a surprise to a man who always had unwavering belief in himself.
And he wants to make sure he is not a flash in the pan.
"It's just about maintaining it, not just for the rest of the season but for many years, hopefully," he said.
"I've always believed in myself to score goals, there's still a lot in my game I need to develop but I can't complain. It's going well.
"There's going to be a lot of praise, you just have to stay focused, ignore some bits and use some bits to lift my confidence.
"I'm just going into every game, believe in myself, block everything out and focus.
"That's what you need as a player to get to the top level. To always believe, even in tough times."