Former Whites head coach Monk was returning to his former stomping ground for the first time since leaving United back in May with the 38-year-old now in charge of Boro.
At a packed Elland Road, the former Whites head coach was subjected to a few boos prior to kick-off and a chorus of chants from the South Stand in particular.
"That wasn't even my focus," he said. "It wasn't about me. It's about my team and the players on the pitch and we're disappointed with the result and should have got more.
"It's not about me. What's happened has happened. I've said my side, the club has said their side and that's done and dusted.
"I've great memories of this club and enjoyed my season here, but now I'm at Middlesbrough and my only focus is on them."
Monk, whose side came in to the game on the back of three successive league wins, felt they did not deserve to lose.
"There weren't many clear-cut chances for either team," he added. "But I think we definitely did enough to at least take a point away from this game."