The pair's British middleweight fight at Wembley Arena was stopped in the 10th round and a few minutes later, Blackwell collapsed in the ring.
The 25-year-old had a bleed on the brain, but is in a stable condition in hospital and reports have claimed that he could be brought out of his coma today.
In Tuesday's press conference, when asked if he considered quitting, Eubank Jr told reporters: "Not all all, this is boxing.
"As fighters, we know the risks. We know that we are risking our health every time we stop in the line, but it's a risk we're willing to take because with that risk comes great reward.
"I will continue my career. I have the British belt and now I want to go for a world title."
During the fight, the boxer's father Chris Eubank instructed his son to avoid hitting his opponent's head and just aim for the body because he feared that Blackwell could get hurt.