The West Yorkshire outfit played out a 1-1 draw with Fulham at home in the Championship.
After a goalless first half, the Cottagers took the lead at Elland Road through Tom Cairney in the 77th minute.
Leeds restored parity in the third minute of injury time when Chris Wood found the net with an overhead kick.
Leeds United's Chris Wood celebrates
Monk has taken to Twitter to give his reaction to Leeds’s performance against Fulham, stating that the display shows the team’s character.
Leeds United's Chris Wood scores
Over the course of the 90 minutes at Elland Road on Tuesday evening, hosts Leeds had just 39% of the possession, took 15 shots of which just four were on target, and earned nine corners, according to BBC Sport.
Visitors Fulham had 61% of the possession, took 21 shots of which only three were on target, and earned four corners, according to BBC Sport.
Leeds will return to action on Saturday afternoon when they take on Sheffield Wednesday away from home at the Hillsborough Stadium in the Championship.