The visitors took the lead in the 40th minute as Darren Bent headed a cross past Mark Bunn, who had erred off his line.
They were not ahead for long, however, as Robert Snodgrass levelled matters on the stroke of half-time with a diving header following excellent wing play from 18-year-old Josh Murphy.
Norwich dominated the second half and they looked set to take the lead when Ricky van Wolfswinkel met Javier Garrido's cross with a powerful header, but Stockdale pulled off an acrobatic save that clearly impressed his manager.
"David Stockdale had a Gordon Banks-like save to keep us in the game," the Dutchman said.
"It was definitely one of the best saves I have seen. It was a fantastic cross by (Javier) Garrido and a great leap by Van Wolfswinkel.
"I honestly thought it was in but it was a fantastic save. That's what makes football so exciting sometimes."
However, Meulensteen was disappointed that his side will now face a replay with Norwich, admitting that having to play another match while embroiled in a relegation battle is less than ideal.
"Before the game all the managers would say, especially the positions we're in (fighting relegation), it's not an ideal scenario but when you’re handed one you have to deal with it.
"We came here to get a result, simple as that. We wanted to progress. We both made changes but it was still a very entertaining game.
"I think it was a bit silly to give away that goal just before half-time through our own mistake in midfield. I think we could have held onto the 1-0 at half-time, then we probably could have got away here with a 1-0 (victory)."
Striker Dimitar Berbatov missed the clash at Carrow Road, but Meulensteen insisted that the Bulgarian was rested rather than injured.
"Berbatov's not injured," he said. "But because of him coming back from injury and being able to play the 90 minutes against West Ham we thought it was better for him to recuperate and be ready for the Sunderland game."
