Speaking to reporters at Wembley, Pochettino said: "We started the game off really, really badly".
"We congratulate them because they are very close to winning the Premier League and after 14 games unbeaten for us, today was a hard game to play. We had the first one against United, we could not do it and now we have another one against Swansea with our 60,000 people and we are going to try to be champion".
Unusually sluggish, Tottenham weren't testing City and, with a swagger back in their stride, Guardiola's men took the lead in the 22nd minute.
As the half wore down, Spurs slightly improved and pulled a fortuitous goal back three minutes before the break when Aymeric Laporte's attempted clearance cannoned off the shins of Christian Eriksen and into the corner of the net.
Pep reverted to a more defensive setup in the second half with the lead in hand, bringing on Nicolas Otamendi for Leroy Sane and resetting his fullbacks to standard positioning. "For him, for the boys, it's fantastic and today he certainly didn't look like he doesn't want to score in the next few games".
Mauricio Pochettino's men came on strong at the start of the second period, but City deserve great credit for eventually re-establishing control and demonstrating the sort of mental fortitude which ensured they held on for all three points.
The South Korea worldwide has now reverted to a wide role and is likely to line up directly against Walker, who left Tottenham past year, in the Premier League on Saturday. Though the foul was right on the edge of the box, the referee pointed to the spot and Gündogan hit a flawless penalty kick to make it 2-0 in the 25th minute.
If Spurs were to add a fourth reversal to that run, then they would restore a 10-point advantage over Chelsea in the battle for top-four finishes.
The Blues went looking for the third goal that would surely end the contest and the superb David Silva saw a low drive beaten away, but despite one or two half-chances, Spurs hung on.
Crystal Palace had been set to drop into the bottom three on goal difference prior to Chelsea's comeback.
They are already all-but assured of Champions League qualification for 2018-19, but still have work to do in order to get over the line.
City were labouring towards a second consecutive draw when Raheem Sterling's deflected strike dolloped past Bournemouth goalkeeper Asmir Begovic to seal a 2-1 win in a breathless finale at the Vitality Stadium in August.