McGhee was forced to make five changes from Wednesday’s goalless draw with Hibernian amid Covid-19 issues and was without 10 players in total.
But Paul McMullan gave Dundee an early lead following Stephen O’Donnell’s mistake and the visitors were well worth their point following Joe Efford’s 18th-minute equalizer.
With Ian Lawlor joining the injured Adam Legzdins on the sidelines, 20-year-old goalkeeper Harry Sharp was handed his first start in senior football.
McGhee also lost experienced pair Charlie Adam and Niall McGinn to injury and was without any center-forwards. Midfielder Declan McDaid was given the lone striker’s role on his first appearance of him since turning out for Falkirk in a loan spell four months ago.
McGhee said: “I think we have to be more than pleased. The young goalie came in, Declan McDaid played up front – not played there and not played since we have been here certainly – and both acquitted themselves very well.
“The others we knew on Friday, but Ian only tested positive this morning. We had to get the young goalie out of his bed and tell him to bring his gloves. I was delighted for him.
“I had hoped that Wednesday would give us a foothold and we could start building. Then you lose five players who started.
“But I think this performance has continued from that.”
Dundee remain bottom of the table, one point behind St Johnstone, who also got a point away against Hibernian.
“There’s a hard road ahead, but we’ve shown in this game that we’re up to it,” McGhee said.
“They can take pride in themselves. After a terrible result against Livingston they have rolled up their sleeves and given two solid performances.”
Motherwell have now gone 10 league games without victory and not opened the scoring in any match since Boxing Day.
This result saw them slip to eighth, but they are only outside the top six on goal difference.
Manager Graham Alexander said: “All the things were there for us, but you have to start well and we started in terrible fashion. Honestly, the goal was so poor.
“It changes momentum, gets our crowd edgy, gets us edgy, makes them puff their chests out and feel better about themselves.
“We responded well and got the goal and we should have then really stamped our authority on the game, but I don’t think we did that.
“We did it in spells here and there, but we never had enough sustained pressure or quality in the final third to get that winning goal.
“It is a missed opportunity, 100 per cent.
“But, amazingly enough, that opportunity is still there for us because of results elsewhere, and that’s what we have got to focus on.”