Kyel Reid's 18th-minute goal settled the replay and booked the Addicks a trip to Corby or Luton, but Elliot had to produce some fine saves including a stunning stop to keep out a free-kick from former Charlton defender Grant Basey.
"I'm pleased to be through in the end," said Parkinson. "On these nights you've got nothing to gain and everything to lose and I can't say it was one of our best performances. It was scrappy from our point of view, but we're through.
"Robbie was outstanding. He pulled off some very good saves. He's taken a bit of time to get his season going and he's had a couple of injury problems but now he's up to speed and he's playing very well.
"He has had some very good performances as of late but obviously he was slightly more busy than he could ever have expected to be - but that's what he's paid for and he pulled off some great saves."
Source: PA
Source: PA