Sadio Mane struck twice in quick succession to hand the Reds their first league win of 2017 at the expense of Pochettino’s second-placed side.
The Merseysiders still remain a point behind Spurs, and 10 behind leaders Chelsea, who have a game in hand, and manager Klopp did not want to look too far ahead.
Klopp said: “What would you think if I said we could get them? Really ambitious or crazy? I am not too interested in this at the moment.
“The only possibility to win something is to win football games. We started, if you want, 2017 tonight. We should not go nuts immediately. Let’s take it step by step.
“Chelsea don’t look like they could struggle over the (remaining) week but we will try everything to get as many points as we can from the season.”
Klopp could find few faults with Liverpool’s display.
He said: “You can win a game and not be happy with the performance but tonight I am really happy with the performance.
“Our offensive part of the game was really strong, really direct, really clear. We showed fight and we played.
“We really concentrated and improved defensively in this game. It was really good and well deserved.”
Mane’s performance underlined what Liverpool missed during their dismal January run when the Senegal forward was away at the African Nations Cup.
Klopp said: “He was fantastic and could have scored a third. It is no problem for me to talk about such a wonderful performance from Sadio but actually, Roberto Firmino, I don’t think I saw a lot of better games from a striker without scoring.
“I saw a lot of good individual performances tonight and that is important, otherwise you can’t win against a team like Tottenham.
“Of course we missed Sadio but each team in the world would have missed him. It is not that we played 20 games really bad, we had a few.
“Now we are back in this race and we have to use this situation. We now have 14-15 days, so two or three days rest for the boys and then a pre-season. We have to use the time.”