Tottenham boss Mauricio Pochettino said he was delighted after his side moved into second place in the Premier League table and that his players believe they can win a first title since 1961.
Following Leicester's brilliant 3-1 win over Manchester City in the weekend's early kick off, the north London side had an opportunity to leapfrog Pellegrini's men and cut the league leaders' gap to five points as Kieran Trippier's first goal for the club sealed a dominant win over Watford.
And, speaking to BBC Sport, Pochettino said: "I feel very proud of the players. We need to be calm.
"We are in a very good position in the league but the philosophy from the beginning of the season has been to go step by step. We are a very young squad so it is important to keep going and take every game and competition and be ready to compete.
"We still need to be more clinical, we created a lot of chances but need to score more."
Tottenham have not been so high in the league with 25 games played since 2012 and Pochettino says his team are now daring to dream.
"You can see in their eyes, the feeling, the energy, that they believe,'' Pochettino told Sky Sports. "In football belief is the most important word. If we believe, anything can happen. I believe in my squad and they believe too in the way we play. This synergy is very important for the future.
"But it is better not to speak too much, only to show, to work hard. This is the better way to show we are ready to compete and after, we see what happens. But the most important thing is to do rather than speak.''
Pochettino's men took to the field shortly after Leicester had stunned Manchester City with a 3-1 win at the Etihad Stadium. Spurs visit City next while Leicester travel to Arsenal in what could prove to be a crucial weekend in the title race. Tottenham have not been crowned champions since 1961.
"It's real we are in a very good position but we need to keep working and not think too much about the future,'' Pochettino said. "For me, historically Tottenham is one of the biggest clubs in England. It is not a surprise we are in a good position.
"Maybe in the last few years, but in the past Tottenham showed they are one of the best clubs in England. Leicester fully deserve their position and how they won the game they completely deserved it because they were better than Manchester City.''
Spurs dominated the Hornets throughout the contest but were thwarted until the 64th minute when substitute Dele Alli crossed for Trippier to slot home his first goal for the club.
Alli had started on the bench after feeling dizzy against Norwich on Tuesday but the 19-year-old took just three minutes to make an impact after coming on as a replacement.
"He is a very good player, a fantastic player,'' Pochettino said. "It was difficult for him Tuesday because he felt bad and it was impossible to play on in the game.
"Today we took a decision to look after him, he is very young. The decision was to start him on the bench and in the second half he made a real impact when he came on the pitch.''
Meanwhile, Watford remain in tenth place after suffering their third loss in five matches.
Hornets boss Quique Sanchez Flores told BBC Sport: "It was difficult. We expected a tough match. Tottenham play really quick, play intelligent balls, they have a lot of good players so it was very difficult to stop their attacks.
"Tottenham have improved since the last time we played. They have more confidence and they are one of the best teams. They have the chance to win the league.
"Playing against Chelsea and Tottenham in four days is too much. We did all the best we could but it was not enough."