The former England striker rescued a valuable point in the dying stages of the Premier League game at Anfield to give the club's survival hopes a boost.
Allardyce admits he didn't see his side getting a point out of the game after Liverpool had gone 2-0 up thanks to second half goals from Firmino and Adam Lallana.
But plucky Sunderland didn't come shirk and came back strongly in the final 10 minutes to secure a point.
Sub Adam Johnson curled in a late free kick before Defoe scored the equaliser in the 89th minute with a fierce strike past Simon Mignolet.
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"The quality of the second goal - nobody could have stopped that," said Allardyce.
"He still has it, we just need to provide him with more chances and he could be our saviour.
"I'm pleased with the new signings who are coming in, making a difference to the squad.
"They have only just got here but staying with the pace of the game, they have done really well.
"I hope their ability continues to shine through as we will need them if we are to get out of trouble."
The Black Cats boss admits he was surprised by the result.
A beaming Allardyce said: "I didn't see that coming. Did you!?
"A bit of quality can always change a game, goals change games. In the end, the last 15 minutes in our favour.
"It didn't look possible when we went 2-0 down, it is a strange old game and never changes!
"We were brilliant against Man City, played better and created more chances. and lost. Here, we defended well until the first goal but didn't defend well defending the second goal.
"Then we had some more belief about us and had some quality goals.
"If you never give up and never say die and have Jermain Defoe up front then you can get something out of the game.
"We deserved an awful lot against City but didn't get it, we may not have deserved this but we took our chances and got a very precious point.
"Coming back from 2-0 down at Anfield in the position we are in is a great compliment to the players for never giving in."