"Listen, what happens on the field stays on the field," Ibrahimovic told BBC Sport.
"I'm not someone who attacks someone off the field. You have the TV, you can see the images. I jump up and jump high and he (Mings) jumps into my elbow.
"It is not my intention to hurt someone. I didn't know about the stamping on the head, if it was him it was him."
Mings also sought to absolve himself of any blame.
Asked by Sky Sports if he purposely stamped, Mings said: "Not at all, I would never do that. That's not in my game. Hard and fair is how I like to tackle but off-the-ball stuff like that isn't in my game."
The result ended a run of six straight wins in all competitions for United and represented a seventh home Premier League draw, with Bournemouth joining Burnley, Stoke and Hull in taking something from Old Trafford.
"The reality is that we are losing too many points at home," Mourinho said.
Elsewhere on Saturday champions Leicester moved closer to Premier League survival with a 3-1 win over fellow strugglers Hull, their second win by that scoreline in as many matches under caretaker manager Craig Shakespeare.
Crystal Palace also moved out of the bottom three with a 2-0 win away to West Brom, while Southampton came from behind to beat Watford 4-3.
Middlesbrough were the big losers at the foot of the table as Swansea moved up to 16th following a 3-2 win over Burnley. Boro went down 2-0 to Stoke and are 18th, three points behind Palace.