Goals from Son Heung-min, Christian Eriksen and a brace from Harry Kane - which saw him become Spurs' all time Premier League leading goalscorer - succumbed the Toffees to a defeat which saw them worryingly unable to record a shot on target.
Big Sam expressed his nerves at the possibility of being dragged into a relegation scrap he had seemingly rescued the club from in his post match press-conference, as quoted by the Liverpool Echo.
He said: "I'm worried about the run we are in at the moment. West Brom becomes a massive game next week so we don't get dragged back into that relegation zone.
"After having a wonderful, wonderful start, we are back on dangerous ground with our results. It's our responsibility to get results to keep ourselves away from that and not wait to see if the others have lost."
The sides went into half-time having performed pretty equally, but the second-half couldn't have been more unbalanced.
"The gulf between the teams was massive tonight. It was a shock second-half performance. I saw some of the good signs of the players last week against Liverpool, and I saw some of the worst signs second half tonight," Allardyce said.
"It was massively worrying in terms of how can a performance become so bad in such a short period of time. Inconsistency leads to poor results, and we've seen a very inconsistent Everton. Obviously, it's something I have to address now. I didn't expect to see it. I've seen it, and I have to address it as quickly as possible."
Everton shots on target in their last five league games:— Richard Jolly (@RichJolly) January 13, 2018
Chelsea (0-0): 0
West Brom (0-0): 3
Bournemouth (1-2): 1
Man Utd (0-2): 0
Tottenham (0-4): 0
Four shots on target in five games.
The one positive to be taken was the performance of new £27m striker Cenk Tosun, who appeared to hold the ball up well as a lone striker, despite a lack of attacking support from his teammates.
Allardyce said: "He was okay. I think it was a very difficult day for him, and a very difficult day for us all in the end. As he gets used to more and more to the Premier League, it's definitely an area of improvement that we need more than anywhere else I think.
"If he can get us holding the ball up, and we can get better service and get the ball in the box like he likes, hopefully he'll do what he's done for Besiktas in their league and in the Champions League."