Villa had taken the lead after eight minutes following Brett Holman’s strike, but Mackie’s header 10 minutes later brought Rangers level.
Mackie has been in good form since Redknapp took over from Mark Hughes, scoring two goals in his last three games.
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“I thought he worked hard,” Redknapp told reporters. “He gives you effort. He runs around. He works hard. He gives you honesty.
“If you had 11 Jamie Mackies you wouldn’t be in this trouble, would you?
“I know just how difficult it is. We must not stand here and kid ourselves. If we pull this one off, my God, it will be a miracle but I believe in miracles so I’ve got to keep trying.”