The Celtic midfielder set the Tartan Army on a course to claim their third straight victory with his cool back-heeled opener in west London, but Michael Uchebo levelled shortly before the break.
An own-goal from Azubuike Egwuekwe restored Scotland’s lead yet they were ultimately denied the friendly win by Nigeria substitute Uche Nwofor on the stroke of full-time.
Mulgrew cut a deflated figure in his post-match interview with BBC One Scotland but admitted it felt good to help extend Scotland’s unbeaten run to a sixth game.
“It feels a bit like defeat to be honest,” he said. “We’re just disappointed to lose the goal right in the last stages when we’d defended like we did.
“We defended well at times but we just need to learn from it and move on.
“We know we can play even better than that so that’s encouraging. There are lots of positives to take from it and when we reflect in days to come there’ll be lots of positives.
“There’s definitely a lot more to do and we can pass the ball better than that.
“We passed the ball well but I think we can pass it even better which is a good thing because it shows we can still get a result and not get beaten.”
Mulgrew sparked the game into life in the 10th minute by connecting with James Morrison’s cross-shot to acrobatically flick the ball into the top right-hand corner.
“I just took a chance because I thought it was going wide and I managed to flick it and it went in,” he added.