The Addicks are now 12 points adrift at the bottom of the table with 11 games to go and appear destined for relegation to League One.
James Coppinger and Brian Stock scored the goals to carry Sean O'Driscoll's Rovers side to a deserved win at The Valley, either side of Nicky Bailey's equaliser.
Parkinson said: "It certainly is a daunting task - we can't hide away from that.
"We have one almighty task on our hands, especially with the other teams winning.
"We had set decent standards over the last three games which we dropped below tonight and we've got to get back up for Watford on Saturday.
"We have got to make the players believe. Let's make sure we don't take 10 steps back from this.
"We need one hell of a run but you have to maintain some belief. I said to the players that between now and the end of the season we put in performances that show more passion and pride than tonight."
Bailey looked to have earned the hosts a vital point with a superb goal but then conceded a penalty to allow Stock to give Rovers a deserved win which should ease any remaining fears of their own.
Earlier James Coppinger had flashed a fine strike inside the far post at the beginning of the second half and give Doncaster the lead their dominance merited.
Parkinson admitted: "We were second best all over the pitch.
"Credit to Doncaster because we came up against a team on form and in the final third we lacked the quality and composure to open teams up.
"We were hit and miss while when Doncaster attacked you felt things were going to happen.
"You can't fault Nicky Bailey. He's got nine goals from midfield in a team at the bottom of the league and if the players had reacted better he wouldn't have been in that position to concede the penalty."
Doncaster boss O'Driscoll insisted that there could be no complaints over the penalty decision which won the game.
A quick corner caught Charlton napping and after Coppinger teed up Richie Wellens, Bailey slid in to block the anticipated shot.
However Wellens quickly shifted the ball out of his feet to induce a foul instead and referee Rob Styles had no option but to point to the spot.
O'Driscoll said: "It was as clear-cut a penalty as you'll ever see. They can't have many complaints over that.
"I'm pleased that in difficult conditions we showed the bit of quality in the game that mattered and we deserved it.
"That's nine wins in 11 games so results wise we've been excellent.
"We've performed well all season but couldn't get the goals. We have always played with confidence so I'm delighted that the players are getting the credit they deserve."