The Black Cats are experiencing a dip in form after a bright start to the season and they have lost five of their last eight fixtures in the league.
Next Sunderland will travel to the Den on Saturday to take on Joe Edwards’ Millwall side, who are also looking to bounce back after two straight defeats in the league.
Mowbray stressed that it is never easy to face Millwall away from home and believes that Edwards’ team will be determined to return to winning ways on Saturday.
The Sunderland boss wants his team to play with intensity at Millwall to end a poor run and prove they remain a good side.
“It is never easy at Millwall, of course”, Mowbray said at a press conference.
“They have lost a couple of games and they will have a real intensity about how they want to try to get back on track, so do we.
“We have to have real intensity to not lose the third game on the bounce.
“Let’s see how it goes; we should look forward to it.
“We know we are a good team in this league, but we have to prove it by sticking the ball in the net and winning matches.”
Sunderland are eleventh in the league table and Mowbray’s side will be eager to turn their form around by defeating Millwall on Saturday.
