Despite having momentum on their side after winning three games in a row prior to the international break, the Smoggies struggled to truly get going in West Yorkshire.
Not until they were two goals down did Boro finally show some sort of response, pulling one back through a Britt Assombalonga penalty and coming close to scoring a leveller late on.
Former Leeds boss Monk remains upbeat on the back of his side's second defeat in seven outings, however, with two big home games against Birmingham City and Derby County to come next week.
"There's a lot of football to be played. You see that week in and week out the changing and the fluctuation of places in the league, how it can change in one game, two games and three games," he told reporters. "It changes all the time. We stay focused and we try to pick up results along the way.
"Off the back of a good run, three wins in a row, I think we deserved at least a point today and I think we will show a good response. We have been really good at home so we can look forward to these next two matches, we had also been on a good run before today in the league and we had a good home win in the last game.
"We want to be strong so we will look to build the momentum again. Whenever you suffer a negative result the response has to be strong. But you have seen the response of the players before, I have no doubts they can respond positively."
Middlesbrough remain in the Championship playoffs, but they are now level on points with Leeds and Derby in seventh and eighth respectively.