Leeds fell behind in the 16th minute when Reading striker Jon Dadi Bodvarsson notched his 10th goal of the season, but they drew level just before half-time when Pontus Jansson fired in from close range.
Pablo Hernandez fired Leeds into the lead 11 minutes into the second half but Reading equalised two minutes later when Eunan O’Kane diverted a Leandro Bacuna shot into his own net.
Leeds have won only once in seven matches since Heckingbottom took over at Elland Road and they are 11 points off the play-offs.
‘The play-offs are out of my mind but they are attainable,’ Heckingbottom said.
‘My mind is on getting the players winning, working with them and pushing them.
‘I want to begin to build a winning mentality because whatever happens this season, if we’re not in the play-offs, we want to be in them next season.
‘So all the work starts now.
‘We worked our socks off to get back into the game today and I thought that we were the better team in the second half.
‘The game started pretty evenly and it was quite an open match. We grew into it after going 1-0 down and were the stronger side towards the end of the first half.
‘In the second half, we wanted to keep the ball more but be very positive with our passing through their midfield to the front four.
‘We should have won really but we haven’t.’
Reading have won only once in 16 league games.
‘I think it was a deserved point,’ said manager Jaap Stam. ‘If you look at how we played in the first half, we were very good at times.
‘We made the right decisions in what to do and when and how to go forward.
‘We scored the first goal and created another couple of very good opportunities.
‘They were 100 per cent chances and we needed to score them. When you can do that, then it’s a totally different game.
‘Leeds came back into it and scored the equaliser, which meant that the game was going to be changing again.
‘In the second half, after we’d got our equaliser, we tried to push forward.
‘But, at times, we couldn’t produce what we’d produced in the first half.
‘It’s a bit frustrating. No one misses chances deliberately but it’s important that when you get into situations like that, you need to finish them.
‘Then you can get closer to the three points that you deserve and maybe need as well.’
Newcastle have been linked with a shock move for former Sunderland goalkeeper Simon Mignolet during the summer.