Sheffield Wednesday scored two late goals at Elland Road to take a 2-0 win over Marcelo Bielsa’s side.
Jacob Murphy netted in the 87th minute before Atdhe Nuhie added a second to seal the points.
Monk was Leeds boss for the 2016-17 season but quit after Andrea Radrizzani completed his takeover of the club.
Wednesday moved up into the Championship play-off places while Leeds’ stutter sees them just six points clear of Brentford in third place.
After the game, Monk said: “I want to win every single game I play in. I’ve done that as a player and I will do that as a manager, it doesn’t matter who I’m playing against.
“I’ve said it all along, whatever club you represent you have to give everything you’ve got and have to show your heart with it. I think that represented it in our heart today.
“Full allocation, a really difficult atmosphere to deal with and a difficult team to play against and we knew that before.
“They key is always to send such a great fanbase, in terms of travelling support, home happy.
“Even if we had lost that game today they would have seen the players that had given everything. I’ve said as much as you would have been disappointed you can live with it and that’s the key to any football team.
“Obviously we are pleased with that result. League leaders away from home. It was a difficult game for us and we knew that coming into it and it proved to be all the way through. They make it very difficult for you. Structurally you have to be very good and organised.
“Most of all, you have to match their intensity and that’s a difficult thing to do at a place like this I know very well.
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“Especially in the second half, we tried to step ourselves up a little bit and we did that. You have to deal with the pressure but then when you get your chances you have to take them.
“I thought they were two really well taken goals and a clean sheet in a very difficult game for us. We have to be very pleased with that result.”
The way in which Wednesday bounced back from three consecutive defeats over the Christmas period was particularly pleasing for Monk.
They had been beaten by Stoke, Cardiff and Hull in the space of seven days before shocking Brighton in the FA Cup last weekend.
“You want to see your players play with heart after the week we had.
“When you play with real heart, you have the courage on the pitch. You feel it and that’s exactly what we needed.