Allardyce was critical of referee Graham Scott's decision to award the Swans a penalty in the first half which allowed them to equalise through Gylfi Sigurdsson before Andre Ayew had the home side head five minutes before half-time.
However, 'Big Sam' was over the moon after Defoe completed his hat-trick, along with Patrick van Aanholt's strike, to give his side a much-needed win.
"I'm not disputing that, it was both ways today," said Allardyce, when asked about the decisions that went in his Black Cats' favour.
"At the end of the day, we've played with the situation as it panned out to come back and win the game. That's all we can do. We had our destiny in our own hands today and we've taken the opportunity to win the game.
"For us, it's an unbelievable win because today if you don't win, then make sure you don't lose. It is an enormous, enormous, enormous three points that gives us a lot of encouragement and hope going forward."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!