Tottenham are fifth in the Premier League, 18 points behind leaders Manchester City, after an inconsistent opening half of the season.
Only last month Pochettino's side suffered a humiliating 4-1 defeat to City at the Etihad Stadium which even put in jeopardy their Champions League place.
Yet, since then Tottenham have managed to recover their best form to secure four victories in the Premier League and one draw – against West Ham - to move level on points with fourth-place Liverpool in the table.
Pochettino hailed his side's response to the disappointing defeat at City and challenged them to keep the current form if they really want to fight for big trophies likes the Premier League or the Champions League.
"The circumstances when you play in a moment and you meet another team, sometimes the circumstances when you play are not the best. It's true that Manchester City are keeping their consistency and level during six or seven months and they're doing so well. If you want to win big things like the Premier League or Champions League that is our challenge," the Tottenham boss admitted as quoted by Football.London after his side 4-0 win over Everton.
"All that we showed today is to show in every week and every game that we play, that's the challenge and our objective and you know that it's tough to keep this type of level over a long period,"
"Against Manchester City was tough. The defeat, I think they were so clinical and I think it wasn't a bad game, only that they were and are in an amazing moment. Then, I think it was so important to work hard and try to keep going and show we can win games and fight for big things. Yes, I think the character is so important always when you receive this type of defeat, and then stand up and start to win again. I am so happy and pleased with the character and personality."
Meanwhile, Pochettino singled out both Harry Kane and Son Heung-min for praise after the two Spurs forwards enjoyed another remarkable performance.
The England international scored two goals in the win over Everton to on 98 after Son had previously given Tottenham a first-half lead.
"He [Kane] is fantastic. He deserves all the credit and a lot of praise. He's fantastic and I'd like to congratulate him one more time of course," Pochettino said before backing the England international to break also the record for goals scored in a single Premier League season at the end of the campaign.
"He can do everything because his mentality and how he is, a professional, he can achieve all that he wishes or wants. Because it's unbelievable the way he is able to work and his willingness. He's always thinking and trying to improve, improve, improve. To score goals and improve with the team,"
"His mentality is collective. That is so important to explain to the people. Yes, he scores a lot of goals but his mentality is to help the team, work with the team and that is what makes him a special player. Not only is he a player with talent that scores goals, in his mind, is always to help and play collectively and put in the effort for the team. Then, of course, he scores goals because he is talented."