The 21-year-old now has seven goals for the season but has yet to be handed a start in the Barclays Premier League, despite outscoring both Emmanuel Adebyaor and Roberto Soldado in all competitions.
Kane struck Tottenham's second goal in a routine 2-0 victory over the Seagulls after substitute Erik Lamela opened the scoring nine minutes after coming off the bench at the interval.
The goal for Kane, who will also have one eye on Roy Hodgson's next England squad, will not guarantee him a start for the trip to Aston Villa on Sunday as he was dropped for the defeat to Newcastle having bagged a Europa League hat-trick three days before.
And Pochettino is keen to keep his options open in attack, despite a clamour for Kane to be given a prolonged run in the side.
"He shares with another striker like Adebayor or Soldado the minutes in the official games," the Argentinian said.
"We need to understand that we are in different competitions
You demand me to play Harry Kane in every game - he played today
Soldado and Harry Kane are different players
We are in a lot of competitions."
Pochettino made 10 changes to the side that was humbled by Newcastle at White Hart Lane on Sunday with only defender Jan Vertonghen keeping his place.
But the former Southampton manager is still targeting success in the competition, with the Magpies their reward for reaching the last eight.
"It's realistic," he said of ambitions to win the tournament.
"We are in the quarter-finals
All potential trophies are realistic
We are in the Capital One and the Europa League and we are happy.
"It was a good performance
We created a lot of chances and played very well
I'm happy for the players because they needed the victory
All players played well."
Pochettino had shown a note of irritation with Lamela, who impressed after coming on for the second 45 minutes, after his compatriot was late out for the start of the second half.
Newcastle's equaliser on Sunday came less than 10 seconds after the restart with Eric Dier only just taking up his position before kick-off - and Pochettino was worried history may repeat itself.
"I got angry, because I was focused and I remembered Sunday," he explained.
"It was because when I arrived to the dressing room we knew it was impossible for (Aaron) Lennon to carry on.
"We told Lamela to warm up
He arrived late to the dressing room and after to analyse set pieces and positions on the pitch he had to go to the toilet, this was the problem."
Brighton, who have not won since their third-round success over Burton, rarely troubled Michel Vorm in the Tottenham goal but manager Sami Hyypia praised the effort of his players.
"We knew that it was going to be difficult to come here," he said.
"Tottenham are a good team with a lot of good players in their side
If they make some changes it is going to be a good player anyway.
"We were thinking we would be on the defensive side and I'm very happy with the work-rate and the effort the players put on the pitch."
Source : PA
Source: PA