The Spurs manager felt his side were capable of much more in his first game in charge since signing a permanent contract to replace Andre Villas-Boas at White Hart Lane
Tottenham - 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 prodded 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."
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."
West Brom caretaker boss Keith Downing, meanwhile, hailed his side's performance against Spurs.
"We had good discipline and organisation and showed big hearts," he said. "We knew we had big characters in the dressing room and they showed that.
"We deserved our point and had better chances, especially in the first half. All in all, there were some really good performances out there.
"The free kick for their goal was harsh but we galvanised really well and responded quickly."