Tottenham begin the New Year just four points behind league leaders Arsenal and could close that gap with a win at Everton on Sunday. They have won their last three matches in a row and lost only twice all season.
Arsenal and Manchester City remain the favourites to be crowned champions in May but neither have pulled away from the chasing pack, while Manchester United and Liverpool are struggling to keep pace with surprise contenders Leicester.
Tottenham's form suggests they could challenge, a theory backed up by their last-gasp win at Watford on Monday, and Pochettino is happy for the club's fans to believe.
"Our supporters are very happy with the team," Pochettino said.
"They share our values. You can see every game at White Hart Lane or away they are unbelievable and back the team.
"It is a very important thing our supporters believe in the team and that we can achieve good things. This is the most important thing. It is the first step to winning some titles.
"We don't set limits on our possibilities. The important thing is we all believe in the way we took 18 months ago.
"We are very ambitious. The group is strong. There is enough quality. In football anything can happen."
Everton are 11th following Monday's 4-3 defeat to Stoke, a loss which means they have managed only three wins in 10 at Goodison Park this season.
Spurs will hope to capitalise on their opponents' stuttering home form but to do so they will have to stop Toffees striker Romelu Lukaku, who has scored 11 goals in 10 matches.
Pochettino admits the Belgian hitman is a threat but believes all opponents are starting to raise their game against his in-form team.
"Lukaku is in a very good moment and is a very good player but Everton have different players who can put us in a very difficult situation," Pochettino said.
"Everton have a very good team and after the defeat to Stoke maybe they want revenge.
"Teams now are very over-motivated to play against us. They know they need to run and be aggressive against us because we are strong.
"But we need to feel confident in our skill and try to win the game. Always in different games you need to try to stop them but it's not different to other games."