Spurs are just one point behind fourth-placed West Ham with three games in hand and they have played four games fewer than Chelsea, who are eight points ahead of them.
But Conte said at his pre-match press conference on Friday that he was not getting carried away by the recent dramatic wins.
"You have to be very calm and go game by game," he said. "Don't forget that we won against Watford in the last minute, we won against Leicester in the last minute, I have to be realistic and for sure I am happy.
"It is a pleasure to see my team fight until the end but if you cut four points off our table and then maybe you don't make this question to me.
"It is important to be realistic and understand it will be very difficult for us this season. It is important to fight and create a good foundation.
"I don't change my idea because of some positive results."
Tottenham have yet to do any business in the January transfer window, although they are understood to have had an offer for Wolves winger Adama Traore rejected this week.
Conte said club chiefs were aware of his requirements.
"For sure, I made evaluations about the squad but I have spoken with the club and I hope the club will listen to me," he said.
Spurs have at least ensured captain Hugo Lloris, 35, will be staying in north London after the France goalkeeper signed a new contract keeping him at the club until 2024.
"It is important our captain has renewed his contract. Not only for one year but for two," said Conte.
"It was right to sign a contract for two years. He is an important goalkeeper in the world, he has won a lot with his national team, he is captain of France, captain of Tottenham."