The Roman side are currently lying in a disappointing 8th place in the Serie A standings, having accrued just 17 points from 13 matches.
The stark reality was not lost on De Rossi, who hinted that a top three spot was probably beyond their grasp, although he added that his team will fight tooth and nail to try and achieve it.
"It would be a real miracle if Roma manage to finish in the top three and qualify for the Champions League. However, we will definitely try to achieve just that," the 28-year-old was quoted as saying by La Gazzetta dello Sport.
De Rossi also pledged his support for under-fire Roma boss Luis Enrique, who revealed earlier in the week that he would be prepared to resign should his charges lose faith in his abilities.
"Luis Enrique? It's hard to compare him to any other coach I know. If I have to come up with a name, I'd say Luciano Spalletti" headed.
"With him, we started playing really well after the Christmas break. Sometimes coaches just need a bit of time."
Roma, who tackle Juventus in their next domestic assignment, are a massive 12 points behind the Turin league leaders.