Pogba sustained a hamstring injury in the Europa League victory over Rostov in midweek and will miss Sunday's trip to the Riverside Stadium along with suspended pair Ibrahimovic and Herrera.
Jones told Sky Sports News: "Middlesbrough have just sacked the manager, so it will probably be even tougher than what it would have been. But we've got more than enough to cope with that. We have strength in depth in this squad and that's why we need everyone.
"There is always an added incentive for everyone playing Manchester United as it is, but when you sack the manager it's even more of a boost for them.
"Especially for the ones who have not been playing in the squad who can force their way into the team and impress. It will be a tough game, but we need to be ready for it."