Spurs made a slow start under the Argentine and had been beaten at home by Newcastle United a week before finding themselves 1-0 down against Aston Villa just four months into his reign.
However, goals from Nacer Chadli and substitute Kane in the final six minutes completed a late turnaround which Pochettino acknowledged bought him time to continue his progression at the club.
"Maybe I can find many other goals that were fantastic but for me the goals are related to emotion, in the period you are living. For me that goal was an amazing goal because it meant for us, for everyone, the possibility to stay here today," he told reporters.
"It's true, the team were 14th or 13th and we were a little bit under pressure because the team were there and playing well, but not win games.
"Always in football, when you don't get good results, the first to be sacked is the manager. That is why that goal allowed us to carry on working and try to change the club."
Kane has gone on to score more than 100 goals for the club, with Pochettino recently describing him as one of the best strikers in world football.