Boro head for Burnley on Tuesday evening having lost six of their last seven Championship fixtures and each of their last six games in all competitions on the road, culminating in Saturday's 4-1 reverse at Crystal Palace.
Mowbray told the club's official website: "It's incredible after the run we have been on that we still find ourselves in the top six and in the fifth round of the FA Cup - but we have to start winning football matches.
"I have said to the players I'm pretty confident we will. If we don't make the top two, hopefully we will make the top six.
"I'm pretty sure we will finish with a strong run, hopefully starting at Burnley. The mood is still positive.
"I tried to give them (the players) an analogy about a boxer getting back up and throwing the first punch again, and I'm sure we will do that and that at the end of the season, we will be looking back on a sticky period in January and February."
Meanwhile, defender George Friend has admitted he loses sleep over defeats.
Friend told the club's official website: "You run it over and over again in your head and just hope you get a chance to put it right when you have another game.
"It was six hours back from Palace, but it wasn't just on that journey that I was thinking about the result. It's when you go to bed at night and on Sunday.
"You don't really stop thinking about it until you start preparing for the next game.
"The only way you can get out of it is to roll your sleeves up and say enough is enough. It doesn't do anyone any good to keep your head down for too long."