"I would never blame a manager...It is always the players," De Roon told reporters. "You cannot sack 25 players but you can sack the manager and hope for something great.
"I think as a team we let the first gaffer down and then we didn't get a win so soon after so I think it is our responsibility and not the coach."
Under Karanka's then deputy Agnew, 19th-placed Middlesbrough ended their 16-match winless run against Sunderland last week before holding on to a 2-2 draw at Manchester City on Sunday.
De Roon believes the recent results have given his side a confidence boost as they remain six points adrift of safety with three games to play.
"Since Steve Agnew took charge he tried to make it more of a team...that is what he believes," he added.
"Winning a game is always a boost so I'm not surprised that after Sunderland we gave a better performance on Sunday."
"It's frustrating and disappointing that this comes so late. All we can do is say we will fight to the end."
Middlesbrough face a daunting trip to league leaders Chelsea on Monday before hosting Southampton on May 13 at the Riverside Stadium. They will travel to Liverpool in the last game of the season.
(Reporting by Hardik Vyas in Bengaluru; Editing by Amlan Chakraborty)
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