Following the game, Mitchell spoke to the press about Rovers' relegation battle, the team spirit at the club, facing pressure in the game, his penalty save and the dressing room atmosphere.
On Rovers' fight for League One survival
"Anything's possible, what's the point in doing anything in life if you don't believe that you can achieve anything?
"We know it's a massively difficult task but we will keep fighting until the end."
Mitchell was asked whether he believed Rovers could still stay up following comments from manager Gary McSheffrey that the team would need five wins to stay in the division.
Doncaster's number 12 was confident that it was a goal that his team could still achieve despite the odds being stacked against them.
It has been a tough season for Rovers, who have picked up just 30 points from the 40 league games they have played this season.
They currently find themselves four points adrift of safety with six games to go in the league, meaning they will need to produce better form than they have been capable of all campaign to stay up.
The team, who conceded six goals in March, scoring none, will need to improve at both ends of the pitch and fast should they want to remain in League One next term.
On whether the team let him down
"No, we're a team, we unfortunately just couldn't get the goal at the end there to get the draw and the point, we'll keep fighting for each other.
"It wasn't just me, Ben Jackson blocked one off the line today which could have kept us in it."
Mitchell was awarded the Man of the Match award in the stadium by the club's sponsors, and his overall performance on the day was impressive.
He managed to get two hands on Washington's penalty, diving left to save it, and made a number of important stops to keep Rovers in the game.
He denied that the team let him down however, pointing to the team spirit at the club as the reason behind why no individual player was responsible for the successes or failures at the club.
The Englishman did also reference Jackson's block off the line early on in the game, which saw the defender hook the ball off the line from a shot which had Mitchell beaten.
Mitchell did also say that he was appreciative to his boss for giving him a run of games between the sticks for his side.
He admitted that his start in goal for Rovers was not good enough and was thankful to McSheffrey for sticking by him in that tough period.
It seems to have paid off for Doncaster, as although the results may not be coming with it, Mitchell gave a performance to be proud of at the Eco-Power Stadium on Saturday afternoon.
On being under pressure in the game
"Yeah we were under a bit of pressure, you could probably say we were a little bit lucky to go in at 0-0.
"I think in the second half we settled and we had some opportunities at the end there."
Rovers were very lucky to go into the interval level, as visitors Charlton passed up on several chances before the break which they nearly paid the price for.
Washington's missed penalty was a key chance for The Addicks which they should have done more with, as well as his missed effort on the slide from inside the six yard box later on.
He missed a header from inside the box, and also hit the crossbar from an open goal at the start of the second half after Washington missed a one-on-one.
From Rovers' point of view, allowing Charlton so many chances would not have been acceptable in what was a shaky defensive display at best from the South Yorkshire side.
It may have also been frustrating for McSheffrey's side that they only managed on shot on target when they were in the ascendancy in the game as it approached its conclusion.
Overall, Doncaster found themselves limited to very few chances in the game which mainly came after they went behind, and were under siege in the first half, which they were fortunate to escape unharmed.
They did eventually have their resistance broken by Stockley's side footed effort however.
On the penalty save
"You do your homework beforehand and try and give yourself the best possible chance of saving it.
"He's [Conor Washington's] taken quite a few penalties over his career so there was a lot to look at."
It was a great penalty save from Mitchell, who was able to claim the ball from Washington's effort from the spot which he had intended to guide into the bottom-right hand corner.
Mitchell was able to guess correctly to make the save, which kept the game goalless at the time.
When asked whether he felt Washington's experience as an international taking penalties made it easier to guess, he said he felt it made no impact on the stop.
He did say that having the extra research available to him from all the penalties Washington had taken did help, but the important thing was making the save on the day.
From Washington's perspective, it was a poor penalty that allowed Mitchell to save with both hands, in what was a disappointing day in front of goal for the Northern Irishman.
Mitchell will not have cared about the quality of the penalty save however, and was pleased to help the team, which unfortunately for him did not help to produce his side any points by full time.
On the dressing room atmosphere
"I think we all are [trying to drag Doncaster to safety], it's not left down to one person.
"The dressing room's hurting after today, obviously after a defeat, but we're all working and grafting away for each other."
Mitchell said that the team are not relying on one player to motivate the rest to keep fighting in the battle for League One survival.
Rovers, who have arguably missed out on leadership since the retirement of club legend James Coppinger at the end of last season, will need all the leadership they can get to get themselves to safety.
So far, the leadership on and off the pitch have not been able to produce an upturn in fortunes at the Eco-Power Stadium.
Despite this, Mitchell believes the right players are at the club to create a good dressing room atmosphere in this crucial stage of the season for Doncaster.