Reading manager Jaap Stam, however, faced up to the prospect of the sack after his side’s woes continued.
The Royals have lost four of their last five Championship outings while their fortunes have plummeted at the Madejski Stadium.
Since a 15-match unbeaten run on their patch came to an end against Bristol City last month, their subsequent three games there have failed to yield a win, with Grant Leadbitter’s penalty and Britt Assombalonga’s header giving Boro the spoils.
“That was an important win for us,” said Monk. “We haven’t been in a good period recently and there’s been a lot of talk about that.
“To put ourselves back on track, we’ve got to strike that right balance between defensive and offensive play. We were very good defensively and were clinical offensively when we needed to be.
“That’s the way to try to build again and we know that, as we get more confident, we have the players to offensively do very well. It was a really good, solid away performance.”
Reading went behind in the 14th minute when Boro captain Leadbitter hammered home from the spot after Joey van den Berg had fouled Assombalonga.
Although Reading dominated for large spells, they created few clear chances. Assombalagona sealed Boro’s victory when nodding home his seventh goal of the season in the 74th minute.
Reading: Mannone, McShane, Tiago Ilori (Blackett 28), Moore, Gunter, van den Berg (Barrow 68), Kelly (Kermorgant 77), Aluko, Swift, Beerens, Smith. Unused substitutes: Edwards, Clement, Popa, Jaakkola.
Middlesbrough: Randolph, Christie, Ayala, Gibson, Da Silva, Leadbitter (Forshaw 76), Howson, Downing, Braithwaite (Bamford 89), Tavernier (Johnson 62), Assombalonga.Unused substitutes: Konstantopoulos, Friend, Fry, Traore.
Referee: O Langford (W Midlands).