David Nugent fired Boro in front from close range after only three minutes for his third goal in four games.
Leeds defender Giuseppe Bellusci then produced a bizzare diving header to divert George Friend's hopeful cross into his own net - despite being completely unchallenged.
Diego Fabbrini scored a gifted third after a Sol Bamba blunder as Mirco Antenucci saw an effort ruled out for a dubious offside.
Aitor Karanka's men spent big over the summer and Rosler thinks the difference in quality showed.
He said: "In many ways the game turned out as I predicted. Middlesbrough didn't create much, but they are very efficient, very deadly because of the quality they have in their squad; Premier League quality. We met a team that you cannot allow too many of the situations we gave them.
"In general we did what I asked my players to do.
"We were on the front foot, we tried to move the ball quickly, to attack them in the right way. In the first half there was nothing between us apart from the first goal and then the first ball into the box we couldn't defend it.
"In the second half we were clearly on top, but the major decisions went against us, which is disappointing.