Spurs saw their top-four hopes dented courtesy of Jake Livermore's late winner at The Hawthorns, leaving them five points clear of fifth-placed Chelsea having played a game more than their London rivals.
A Champions League place remains in Tottenham's hands heading into the final two games of the season, and Pochettino is confident that his side do not need to be reminded that they still have work to do.
"I don't believe it's a wake-up call. If we need, after 36 games, someone to say 'hey, come on, we need to win, we need to be professional and play with the right attitude' we need to go deeper and assess why," he told reporters.
"Everyone can see the game, we dominated but if you are not clinical in front of goal it's always open. We didn't create enough chances, maybe we created more (than West Brom) but we're a team who need to create more to have the capacity and then to score.
"It's still in our hands so we need to work hard in the next two games but it's our chance to be in the Champions League next season."
Tottenham's last two games of the season come at home to Newcastle United and Leicester City.