In front of a crowd of 7,013, the Falcons were trailing 16-9 with three minutes to go in Friday night's Aviva Premiership clash at Kingston Park, and were looking a poor second to the Warriors.
But suddenly, the Newcastle pack found another gear and drove Mike Mayhew over for a try which Jimmy Gopperth converted to level the match.
The fightback will have been heartening for Tait, who revealed that Newcastle would officially announce the signing of Stormers second-row Adriaan Fondse on Saturday - a deal that is likely to be the first of many in the coming months.
"It's two points that will help us no end," said Tait. "We should have been fast out of traps but we were very nervy and we only seem to start to play when all seems lost.
"We have to start believing in ourselves. We have a fantastic squad but they have the realise that this is only November and not April and stop being so nervous.
"We will add to the squad with the signing of Adriaan Fondse, who is a big ball-carrying line-out player, and there are more on the way because our new owner has been fantastic and is giving us real backing."
Worcester opened the scoring with a Joe Carlisle penalty after five minutes when Ally Hogg strayed offside but Hogg made amends with a pulverising drive which Jamie Helleur and Crone Uys carried on to win a penalty which Gopperth knocked over for 3-3 after 12 minutes.
Carlisle's high kick was taken by Greg Goosen but the Warriors pack turned it over and Newcastle were offside again for Carlisle to put Worcester back in front at 6-3 in the 20th minute.
But Worcester conceded a soft penalty at the line-out two minutes later and Gopperth levelled the scores.
Newcastle were struggling to find any distance with their kicks and an appalling slice from Rikki Sheriffe allowed Worcester to drive into the Falcons 22 and Shaun Perry looped around Carlisle with the fly-half offloading in the tackle for Perry to score, and Carlisle's conversion in the 27th minute put the Warriors 13-6 ahead.
Newcastle tore into Worcester early in the second half to gain a penalty after seven minutes which Gopperth kicked for 13-9 to give the Falcons hope.
Alex Tait scythed through the Warriors defence and a try seemed certain but Uys just failed to hold the pass which Tait popped up as he was hauled down inside the 22. With 12 minutes left Andy Goode kicked a 45-metre penalty which looked to be the final act until that dramatic match-saving effort from the Falcons.
Worcester head coach Richard Hill said: "Our players are very disappointed they didn't close out the game and I've been consoling them - which is a bit of change - and telling them it is a good two points.
"But we do tend to sit back on a lead and we have to stop doing that and get a winning mentality."
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