Simeon Jackson's 70th-minute header looked like it would be enough before Pools right-back Neil Austin fired home from 20 yards to ensure a draw.
Both sides cancelled each other out in a drab League One affair, and Stimson admitted: "We dreamed we were going to win. We always dream every night, but sometimes dreams aren't as nice as you would like them to be.
"We were close, very close after scoring a fantastic goal. Rene Howe worked the channel well for Jackson to score a fantastic goal and we thought it was going to be our night.
"At least a point is more than we have been getting away from home this season. Again it was a whole-hearted, committed performance, with signs of quality in there and we look forward."