Spurs benefited from a dubious penalty decision in a highly-charged Barclays Premier League clash at the Etihad Stadium but Christian Eriksen's 83rd-minute winner lifted Pochettino's men within two points of leaders Leicester.
City had fought back after Harry Kane's disputed spot-kick to level through Kelechi Iheanacho but a late lapse allowed Eriksen to pounce, snatching victory and damaging the hosts' own title hopes in the process.
Pochettino refused to get carried away as Spurs enhanced their prospects of a first league championship since 1961 but he accepted it might be a different story for success-starved supporters.
He said: "It is true that our supporters can dream, this is important, but for us we start to prepare for the (Europa League) game against Fiorentina.
"Like always, you need to work hard and try to improve every day and we are now in a good position in the table, but is too early to start to speak about the title."
The first half was keenly contested but lacking in clear-cut chances
The complexion of the game changed dramatically after the break as Raheem Sterling was harshly ruled to have handled inside the area as he turned his back to block a Danny Rose cross.
There was intense debate over whether it hit his arm at all, or how it could even have been deliberate
It was also only just inside the box
Kane brushed aside the controversy to register his 19th goal of the season.
City rallied and hit the bar through Yaya Toure before Iheanacho lashed in a fine leveller.
But as City pushed for a winner that would have lifted them within three points of the top, Toure lost possession and Erik Lamela charged forward to set up Eriksen.
City manager Manuel Pellegrini criticised referee Mark Clattenburg after a penalty incident that brought back bad memories of two contentious offside decisions in the 4-1 loss at White Hart Lane in September
Pellegrini said: "Unfortunately for us it was the same referee, Clattenburg, as when we lost against Tottenham in the first (game) with two clear goals offside."
It was another bad result after last week's comprehensive and equally damaging 3-1 defeat by Leicester
City have drifted from being title favourites just over a week ago to fourth on the bookmakers' list but Pellegrini is confident his injury-hit squad can still recover from the damage.
He said: "The last two results we had here at home were very bad
We never expected not to win a very important six points but we must continue fighting
"It is very important to start working again and believe all things can happen."
Source : PA
Source: PA