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.
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“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 Preston North End legend Sir 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.”
Meanhile, Raheem Sterling criticised the fans that jeered Joe Gomez against Montenegro, with manager Gareth Southgate saying that “no England player should ever be booed”.
The build-up to the Three Lions’ chance of sealing Euro 2020 qualification in their 1,000th match was overshadowed by a skirmish at St George’s Park on Monday.
Sterling made private and public apologies after emotions got the better of him less than 24 hours after clashing with Gomez towards the end of Manchester City’s 3-1 loss at Premier League leaders Liverpool.
The 24-year-old (below) was made to watch Thursday’s match against Montenegro from the stands as punishment, with Kane’s hat-trick helping England seal a 7-0 win – their biggest at home since 1987 – and top spot in Group A.
Gomez was brought on as the Three Lions’ final substitute in the second half at Wembley, where the defender was surprisingly jeered by pockets of supporters.
Sterling, who applauded his team-mate on to the field, posted on Twitter: “To all the England fans, I wanted to leave things as it was but tonight I have to speak again.
“It was hard for me to see my team-mate get booed for something that was my fault. Joe hasn’t done anything wrong and for me to see someone who keeps his head down and work hard...
“Especially after a difficult week for him to be booed when he came on tonight was wrong. I’ve taken full responsibility and accepted the consequence. I felt as though I had to say this, get home safe everyone.”
England manager Southgate echoed Sterling’s sentiments in the post-match press conference.
“I don’t know what more I could’ve said,” he said.
“Again, first and foremost, the whole dressing room are disappointed with it because the dressing room are tight, every one of them.
“Contrary to what I’m told has been said in various quarters, all of the players are united, the whole thing was put to bed the other day.
“Joe had done absolutely nothing wrong. No England player should ever be booed when they’re wearing the shirt, ever. I don’t get it.
“So, all of the players are particularly disappointed with that, and the reason that I wanted to get Joe on the pitch tonight was that he’s been with us in September and October and we’ve not got him into the games. Also, I know I’m going to start Raheem on Sunday and get him back on to the pitch as well, because it was important for both of them to get back on the field with England and show everybody that we’re all in this now.
“So, yes, I’m hugely disappointed for him, but he’s got the support of all of us – the whole dressing room, totally united. And we’ll make sure we’re there for him.”
Asked whether he will speak to Gomez about the issue, Southgate said: “Absolutely. I’ve already started that, and yes, he’s got to feel the support of everybody, which he has, completely.”