Following a goalless first half, Ramires's shot flicked off Fernando Torres on its way to goal for the opener and the visitors made sure of victory 15 minutes from time when substitute Eden Hazard laid a second on a plate for Victor Moses.
Boro had given as good as they got for long periods and Mowbray said: "We have got 12 games left now. For six months of this season, we have been in the top six and we have been threatening the top two for most of that time.
"We have obviously fallen off the pace in the last six weeks, for whatever reason, be that injury or the fact we have been involved in cup competitions.
"But we have to get back to business now. We have to start winning football matches again now and our only concern this year is to try to get out of this league."