The Teessiders entertain Barnsley on Saturday having battled their way clear of the drop zone and Mowbray is hoping the confidence they have gained will serve them well as they plot a future promotion drive.
He said: "Playing under pressure is not bad for a team to develop team spirit and camaraderie when you have to find performances and have to get results in big games.
"We are at the wrong end of the table doing that but hopefully somewhere along the line there will come a time when we are playing big games.
"I have been watching Champions League games in recent days and the pressure on those players to get to semi-finals and finals on top of trying to get points to stay in the top four or win leagues, that's a huge pressure.
"We are at the other end in huge games trying to pick up points but somewhere along the line we hope to get to a scenario where the huge games are about staying in the top six or staying in the top two."
Source: PA
Source: PA