Darren Bent's opener was quickly cancelled out by Robert Snodgrass in the closing stages of the first half before David Stockdale made a miraculous one-handed save to deny Ricky van Wolfswinkel from six yards out.
Meulensteen said: "We didn't want it (a replay), I think Chris (Hughton, the Norwich boss) didn't want it either, but that's how it turned out. A draw's a good result away from home.
"David Stockdale had a Gordon Banks-like save to keep us in the game.
"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."
Opposite number Chris Hughton praised Stockdale for the stop.
"Outstanding," the Norwich boss said. "From the angle we had we thought it was in. It's a wonderful save."
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