Kevin van Veen's first-half penalty was saved by United keeper Carljohan Eriksson, while Motherwell's top scorer also hit the bar and missed a close-range header as his side endured a frustrating afternoon in front of goal.
The Tannadice caretaker handed the plaudits to Steven Hammell's rejuvenated Well and believes the result could be a starting point despite still searching for a first cinch Premiership win of the season.
Fox, 38, has been placed in temporary charge of United after the dismissal of Jack Ross and will wait to see what managerial decision is taken by his club.
He said: "It's been a tough week, a long week for everyone connected with the football club. I'm not being negative and saying we are coming here accepting a point, but the reality of this week – Wednesday, today and the limited time on the training pitch, we are reasonably pleased with where we are at.
"I've been totally focused on Wednesday and today. I'm sure, at some point, I'll speak to whoever I need to speak to. The club is going through their process and, moving forward, that's something well above my pay grade. Until I'm told otherwise, I'll just carry on.
"It's a long time until we set foot back in the building as the boys have got a day off tomorrow. A lot can happen in that period of time."