Totteham - under the permanent leadership of Sherwood for the first time - took the lead in the 36th minute at White Hart Lane through a Christian Eriksen free-kick, but were soon pegged back by the visitors.
Jonas Olsson prodding home from close range two minutes later following a set-piece, and Sherwood was unhappy with the dropped points.
"I'm disappointed," he said. "I thought we were better.
"It was a poor free-kick to give away and we were unable to clear it. It was a kick in the privates to be honest.
"The fans will be disappointed. With respect to West Brom, I think it's a game we should have won.
"But, also, I maintain it's a game we should have played better in."
The head coach, who was named as Andre Villas-Boas' successor on Monday, feels he has not yet had enough time on the training pitch to implement his own methods and ideas.
"We had no time to really work on the training field because the games are coming thick and fast," he added.
"We've got as much as we can into them and we'll only improve."
Sherwood is adamant he has what it takes to succeed at Tottenham, despite his lack of managerial experience.
"To manage Tottenham brings its own pressures and to play for Tottenham brings its own pressures," he continued.
"You have to win, especially in front of your own fans.
"Of course there's an element of a gamble (about his appointment) because I've never done it before.
"But I think there's a lot of good managers who've never done it before and have been a success."
