The Teessiders are 10 points clear of the npower Championship relegation zone after Saturday's 1-1 home draw with Barnsley with most of the clubs below them having just four games left to play.
They last lost at Reading on March 5 and know victory at Burnley on Tuesday night will leave them mathematically safe.
Mowbray told the club's official website: "That's seven games unbeaten from a team that for most of the season have been relegation threatened and I would never sit here and give this team any criticism.
"For them to string together that sequence of results shows a great desire not to lose football matches."
The trip to Turf Moor represents 18th-placed Boro's game in hand on the bottom five.
Source: PA
Source: PA