Goals from Heung-Min Son in the first minute and a Harry Kane brace (8th and 16th minutes) sent Spurs in 3-0 up at the break and in cruise control against the Hammers.
Spurs held a 3-0 advantage until the 82nd minute, when Fabian Balbuena scored what looked to be a consolation for the visitors.
An own goal from Davinson Sanchez and an injury time long-range strike from Manuel Lanzini completed a remarkable comeback for West Ham and ensured a share of the spoils in the Premier League game.
Warnock, who was watching on for BBC Radio 5 live, thinks that the result puts question marks over Tottenham’s mentality when considering whether or not they could challenge for the title.
He said: “Can Tottenham go on and challenge for the Premier League?
“What we have seen in that second half is that they are vulnerable defensively.
“The mentality of the players is perhaps not strong enough to do that.
“Management of a game is huge”, Warnock added.
Tottenham will have an opportunity to return to winning ways later this week when they play host to Austrian side LASK Linz in the Europa League.
Their next Premier League assignment is away at Burnley next weekend.