Bale had earlier opened the scoring for Spurs, but his biggest contribution came at the end as he thumped in a wicked 30-yard effort which nicked the points.
And Allardyce was left in awe, saying: "If you get too tight he skips past you, if you stand off him he hits them like that (the winning goal).
"You have got to admire the quality of the goal. We've heard a lot about Michu at Swansea and what (Robin) Van Persie has done for Manchester United but at the moment there's nobody doing more for a football club than Gareth Bale for Tottenham, by the quality of goals he is scoring and consistent level of goals.
"I am not sure anybody else has scored for them recently, and every goal he seems to be getting is outside the box as well."