Rovers led at the interval but the visitors hit back with a vengeance to score three second half goals.
Adkins said: "We weren't at our best in the first half but we had words during the interval and the response from the players was fantastic.
"There's a hunger and a passion about this side and it's in our own hands whether we are in the play-offs or not.
"We've got Burnley at home in the last match and that won't be easy but I'm expecting a full house and we will be going all out to win the game.
" We fell behind in the first half today to what was a poor goal from our point of view.
" We've only come from behind once this season - and that was in the first match - so it was overdue.
" I reminded the players of that at half-time and I couldn't have asked for a better response.
"We made changes and Jake Taylor, who has been at the club since he was eight years old, came on to deliver the cross for us to take the lead.
"We've been decimated by injuries since September but Pavel Pogrebnyak came in today and scored two great goals.
"The whole group contributed today and that's what's got us where we are this season.
"We knew we had to win to keep our season alive and the players have gone out and done that."
Rovers were much the better side before the interval and deservedly snatched the lead when James Coppinger latched on to a cross from Billy Sharp to fire home in the 25th minute.
Reading looked a different side after the interval but it needed a penalty for them to land their first shot on target when Adam Le Fondre equalised from the spot in the 63rd minute after being brought down by Paul Quinn.
Both sides tried to snatch a winner and Pogrebnyak turned up trumps for the visitors when he headed them in front from Taylor's cross in the 87th minute before putting the issue beyond doubt deep into stoppage time.
Disappointed Doncaster boss Paul Dickov said: "We were all gutted in the dressing room afterwards but we will get it out of our systems before we go again in the final match at Leicester.
"We came out fighting in the first half and put ourselves in a good position with the goal but you have to give Reading credit for battling back.
"I didn't have a clear view of the penalty incident so I can't comment on that but the other two goals they scored were poor from our point of view.
"We didn't allow them to play in the first half but we went a little gung ho after they had equalised from a penalty that came from a goal-kick.
"A point might not have been a bad result for us as it happens but we went for it and had a go.
"Now it's all down to the last match against my old club - who won't be doing us any favours - but I'm still confident we can avoid going down.
"There was drama at this club on the last game last season when we went up by winning at Brentford and there can be drama again at Leicester.
"Whatever happens, we'll go there and give it all we've got because we want to stay in this division - and we can't rely on other results going our way."