The 21-year-old ended his long wait for his first Chelsea goal in their 3-2 victory over Norwich City in Saturday’s Premier League game.
The youngster scored a brace against the Canaries to help Frank Lampard’s men clinch their first win of the season at Carrow Road.
Last season, Abraham racked up 25 Championship goals while on loan at Aston Villa to help the Claret and Blue Army gain promotion to the English top-flight.
Despite the impressive showings, the 46-year old believes the young striker is still a work-in-progress and must emulate former Chelsea goal poacher Costa, who bagged 52 league goals in 89 appearances during his three-year stay at Stamford Bridge.
“Let's give Frank Lampard credit for the way he secured his first Premier League win as a manager at Norwich,” Redknapp told Daily Mail.
“There was pressure on his side to win but Lampard had the courage to start with Tammy Abraham upfront and his bravery was rewarded as the 21-year-old got two goals.
“Abraham is not the finished article. I think he needs to be nastier and a master of the dark arts like Diego Costa. Then maybe the No 9 shirt will be his for the foreseeable future.”
Abraham will hope to inspire Chelsea to victory again when they take on Sheffield United in their next league game on Saturday.