Jack Byrne's 35-yard drive earned Redditch United another important point in their bid to pull clear of the Blue Square North relegation places.
The Reds held their lead until the hour-mark when Tamworth levelled the game through Richard Tait.
Redditch player-coach Carl Heggs told BBC Hereford & Worcester he felt they could easily have won the game.
"In the second half they were lumping the ball forward and we were camped in a little bit," he said.
"But we hit sides on the break and I thought we were going to get our second goal by doing just that."
We're aware that we probably need another point from Hyde on Saturday
Carl Heggs
Redditch must thank striker Gary Hay for some vital goals since coming in to help in their relegation fight, but he will be having nightmares over his last-gasp miss with the final kick of the game.
After robbing the Tamworth keeper wide out, Hay took the ball into the six-yard box but, completely unchallenged, he somehow managed to blaze the ball over the bar.
Heggs said Hay knows he could have banished any lingering relegation concerns but insisted the striker must not dwell on his miss.
"It was hard to believe to be honest," he said. "But he has chased a lost cause and made everything happen himself.
"He has pushed it to three yards from the goal line and we are all turning and celebrating, but he hits it over the bar.
"It was unbelievable but his contribution since he has come here has been absolutely great - that's football."
Redditch are now six points clear of the relegation places with only three matches remaining.
And Heggs added: "We're aware that we probably need another point from Hyde on Saturday.
"We'll be coming in on Thursday and working on our shape and set-pieces and we'll be absolutely ready for the Hyde game.
"If we can get any sort of a result against Hyde, then it is all over."
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