Christian Eriksen's stunning free-kick, which curled over the Albion wall and in off the underside of the crossbar, broke the deadlock on 36 minutes.
But the visitors, who played a five-man defence with three centre-backs, levelled the score just two minutes later when Jonas Olsson pounced on some sloppy Spurs defending to stab the ball home from close range.
The hosts played with more freedom and fluency than under previous boss Andre Villas-Boas - but struggled to find a way through a firm Albion backline marshalled well by the impressive Olsson.
Kyle Walker and Danny Rose impressed in attacking full-back roles, and Sherwood admitted the Baggies deserved some credit for earning a draw.
The 44-year-old has been appointed as Tottenham head coach until the end of the 2014/15 season, and he said: "I'm disappointed with the result - obviously I want to be winning our home games, but give credit to West Brom, they've come and done a job.
"They've played with three centre-halves and stuck a lot of bodies behind the ball - and we knew it would be that way.
"I thought we could have played better, especially in the first half.
"In the second half we were relentless in attack and put a lot of balls into their box, and on another day it might have fallen for us and we could have scored some more - but it wasn't to be and we've got to crack on to the next one."
Sherwood added: "I thought we created some chances in the second half - but I'm always seeking perfection and we could have probably had a bit more guile around the edge of their box and risked the ball a bit better, and also we can improve on winning the ball back a little bit further up the field.
"It's been difficult because we haven't been able to get any time on the training field with games coming thick and fast - but we will, and it's a new voice for the players and to play a different way, and hopefully they will improve, as they need to."