Chris Cohen's goal proved the difference between the two sides in a hard-fought Championship clash that ended with the Reds moving back into a top two position.
"I could not see them scoring but, fair play to them, they came up with the one goal that mattered," said Strachan, who felt that Forest had all the 'breaks' during the 90 minutes.
For 'Boro, a second away defeat of the week sees them slip to ninth in the table, four points off the play-off places.