Eric Dier sealed a fairytale debut by scoring a stoppage-time winner in a dramatic opening-day encounter at Upton Park on Saturday.
West Ham also had James Collins sent off later in the clash, and Pochettino says that the Premier League's elite will have taken note of his team's resolve.
"We sent out a signal to our opponents and to us too," he is quoted as saying by The Mirror.
"We managed to win and that was our signal after Kyle Naughton was sent off. This was important. We showed belief and we showed character."
Pochettino's side host Queens Park Rangers at White Hart Lane next Sunday.