The bitter rivals played out a thrilling 2-2 draw in one of the most important North London derbies in history with both sides vying for the title.
The result, and Leicester City's 1-0 win over Watford, means Mauricio Pochettino's side trail the leaders by five points and Arsenal by eight with nine games remaining.
BBC pundit Shearer, who scored 313 goals in 622 career games for club and country, was impressed with Arsenal but told Match of the Day the game all hinged on Coquelin's 'stupid' challenge.
"Arsenal very much frustrated Tottenham like West Ham did in midweek," Shearer said on MOTD.
"Then this (Coquelin's red card) happens.
"I mean it's a stupid challenge, what on earth is he doing? Harry Kane is going absolutely nowhere there, he's on the touchline, then the game changes.
"Arsenal were comfortable from set pieces until that point.
"Having said all that I've got to give credit to Arsenal for the way that they battled back and a draw really didn't suit either team."
The real winners this week have been Leicester after Spurs lost to the Hammers 1-0 in midweek while the Gunners were beaten 2-1 at home to relegation threatened Swansea City.
All still to play for, but Spurs have it easier
Arsenal will now try to build on their battling draw by reeling their rivals in over the coming weeks.
It is all still to play for, but Tottenham will be confident of a return to winning ways when they travel to Aston Villa before entertaining Bournemouth in their next two league games.
That is sandwiched by their two-legged Europa League last 16 game against Borussia Dortmund.
Arsenal meanwhile have a tougher schedule with an FA Cup replay against Hull City they could do without up next in midweek.
That's followed by games against a rejuvenated West Bromwich Albion, Everton, Watford and West Ham looming either side of their second leg encounter with the mighty Barcelona at the Camp Nou.