Only promoted pair Reading and West Ham had a better away record than Middlesbrough in the Championship last season and Mowbray is hoping his side can repeat their fine start to the new campaign.
Mowbray told the club's official website: "It's a cup competition and you get what you get and we'll expect a very tough game from a team who finished in the middle of League One last season.
"It's before our league season kicks off, but hopefully we'll be ready and we'll do as we did last season at Walsall and be as professional as possible.
"Let's see if we can start the season away from home like we did for most of last season, with a good result."
