United conceded their 22nd and 23rd goals of the season inside the first 20 minutes before levelling it up before half-time but Mourinho refused to blame the system or his makeshift defenders for another slow start.
Still seventh in the table, the Red Devils could end the weekend nine points off the top four.
Whilst United can't move off a goal difference of -1 (-1!), their fans have had to watch rivals Manchester City once again score an abundance of goals, at 43, nearly double the tally United have wracked up, and top the EPL table.
Six minutes later, it was 2-2 when Rashford got to the byline and cut the ball into the six-yard box, where Herrera nipped in front of his marker to score with a cute back-heel that McCarthy got a hand to but could not keep out.
Sanchez is furious with Mourinho for dropping him for the champions league clash with Young Boys on Tuesday. But who will Jose Mourinho start in a must-win game for United? Can we go there and bring those players here? No.
"With all the respect, we don't have many mad dogs that bite the ball and press all the time we don't have many people with that spirit".
UEFA statement on FC Vorskla v Arsenal FC match
They are coming with us because we can give them chances tomorrow and also because we would prefer for some players to not do this long travelling.
"By losing so many balls in midfield, we broke that dynamic that normally leads to goals".
And outstanding free kick put United in real danger, as Cedric Soares dipped a vicious effort over the wall and inside the near post.
The equaliser was all about the tenacity and direct running of Marcus Rashford, who brilliantly supplied Herrera for his well-taken first goal of the season.
United's next league encounter comes against Arsenal at Old Trafford in midweek and it remains to be seen whether the likes of Chris Smalling and Eric Bailly return to the mix after missing the Southampton game with foot and back injuries respectively.
"Second half there was not a lot of momentum generated by United, that's credit to us", Southampton manager Mark Hughes said.
Southampton were denied a late victor as Nathan Redmond brought the best of out De Gea, leaving United sitting seventh in the table and with a negative goal difference.