Mid-table United appeared on course for just a second victory from their last 14 games after a superb strike from Pablo Hernandez put the Whites 2-1 up at hosts Reading with 34 minutes left.
The Royals had led 16 minutes in after Jon Bodvarsson finished an incisive breakaway, but Jansson tucked away Adam Forshaw’s cross to level matters two minutes before the break.
But within two minutes of Hernandez putting them in front they allowed Reading to equalise when a Leeds free-kick led to a Royals counter that ended with Eunan O’Kane diverting Leo Bacuna’s cross into his own net.
Neither side was able to bag a winning goal as former leaders Leeds slipped to 13th and 11 points off the play-off spots with just nine games to go, having won just once in 2018.
“At the moment I feel ashamed,” said Jansson. “In 2018 we have one win and I am born to be a winner and win games.
“That’s what I live for, that’s why I play football, because I want to win games and we have one win in 2018 so I feel bad. It’s difficult to put words on it.
“I came to the club last year and I had a good season and this season has also been good, but now we have won once in 10 or 15 games and that’s not good enough.”
Reading dominated after an early chance for United’s Gjanni Alioski and only some smart saves from young goalkeeper Bailey Peacock-Farrell kept the Whites in the game.
United, backed by almost 3,500 fans, improved in the second half with both Alioski and Pierre-Michel Lasogga going within inches of bagging a winner.
Alioski was denied by a fine save by Reading goalkeeper Anssi Jaakkola, who was later relieved to see a clearance that had been charged down by Lasogga trickle onto a post.
Jansson added: “Now it’s up to everyone to show grit and prove they want to stay and play for Leeds. They have to show it now on the pitch.
“We said that the play-offs is not something that we have to think about now. We have to take it game by game and, of course, think as a team, but also individually.
“We said that if you want to be here next season then you have to prove it on the pitch and I think we took a step forward towards doing that (at Reading). We showed more character than in recent games.”
Reading: Jaakkola, Gunter, Moore, Ilori, Bacuna, Clement (Swift 63), Evans (Edwards 63), Kelly, Aluko, Barrow, Bodvarsson. Unused substitutes: Mannone, Blackett, Smith, Loader, Holmes.
Leeds United: Peacock-Farrell, Berardi, Pennington, Jansson, De Bock, O’Kane, Forshaw, Alioski, Hernandez (Dallas 85), Saiz, Ekuban (Lasogga 77). Unused substitutes: Wiedwald, Anita, Pearce, Phillips, Vieira.
Referee: S Duncan (Northumberland).