The England striker was rested for the fixture as Fernando Llorente was given an opportunity to lead the line, and he duly delivered with a hat-trick, with a Serge Aurier brace and a Son strike effectively ending the game as a contest.
However, on 76 minutes Kane was introduced despite the 6-0 scoreline and the Englishman notched a seventh six minutes later.
Pochettino defended his decision to risk his top scorer for the final stages of the game, insisting he felt Tranmere were entitled to see one of Europe's top marksmen in action.
"It was respect," Pochettino said after the game.
"Respect the people, respect the opponent. They're not going to have many chances to see Harry Kane play here in a competition like the FA Cup.
"I think it was a great atmosphere. For different reasons, I decided to make a change and put Kane on the pitch but one of them is that.
"It's important to show respect to the people here so they could see Harry Kane, who is an icon in English football. It is difficult in that division to see it. It was important to see him in action."
Pochettino also asserted the seriousness with which the club is approaching the FA Cup, with Tottenham desperate to end a barren run of 10 seasons without silverware since an extra-time League Cup victory over Chelsea in 2008.
"Like all the competitions, we take it very seriously," he added.
"Of course sometimes you can win and sometimes you can lose, but always we are serious and respect the competition.
"It's important for him [Kane] to score and have 20 minutes playing football and for the team to get to the next stage of the FA Cup.
"It was an important fixture for the club. To be in four competitions is an important thing."
Tottenham take on Chelsea next in the first leg of their Carabao Cup semi-final.