The 22-year-old enjoyed a prolific start to the season but found himself behind Olivier Giroud in the pecking order by the end, though finished with a respectable tally of 15 Premier League goals in 34 appearances.
His goals throughout the season played a crucial role as Chelsea sealed a top-four finish and reached the final of the FA Cup as well as the last 16 of the Champions League.
However, with Chelsea signing Werner in a £53million deal, alongside the acquisition of Hakim Ziyech, Abraham's opportunities may be increasingly limited next season.
The forward insists he is relishing a new level of competition, believing the calibre is nothing more than expected at Chelsea.
"This is Chelsea Football Club, there's always going to be high standards and high competition and this is something I've been dreaming of since I was a kid," Abraham told The Telegraph.
"I've always been fighting for it, it's never come easy, it wasn't easy at the start of the season but I worked my way into the team and that's what I've got to keep doing.”
Chelsea's season came to an end as they exited the Champions League with a 7-1 aggregate defeat to Bayern Munich on Saturday.
Abraham scored the Blues' one consolation goal, however, and subsequently revealed Robert Lewandowski - who scored his 53rd goal of the season on the night - as an inspiration of his.
"We're a new young side, with a new manager and so we have to be pleased with ourselves," he added. "But this is the level, it's where we have to get to and better.
"For me, Robert Lewandowski is the best striker and that's the level I've got to get to and better and that's what I am inspired to be.
"It's been a great learning curve, great experience for me and upwards going into next season. I've got to build myself up to those high levels.”