Wes Fletcher set up a replay with his 86th-minute tap in which came after the out-of-sorts Mildenhall spilled a right-wing cross from Lanre Oyebanjo.
Goals from Eliot Richards, Matt Harrold and Chris Beardsley looked to have been enough to move the Pirates into the second round but, despite having to settle for a replay, Ward stood by his shotstopper.
yards after 41 minutes to give the visitors the advantage at the break.
"Steve has been my most consistent player since I returned to the club and I'm not going to carp about a couple of uncharacteristic errors," he said.
"There were so many positives in the game for us, but at the moment there is a feeling of disappointment because I didn't want a replay.
"Matt Harrold has had a frustrating time with injury and his goal really lifted the place. We now have good competition for places up front, which is encouraging.
"Not so long ago we would have taken a 3-3 draw with anyone. Things are going in the right direction and we are in the draw for the second round, which is the most important thing."