The young striker had an early penalty saved at White Hart lane on Thursday night, but bounced back to tuck away the opening goal and set Spurs on their way to a 3-0 aggregate success which secured their place in the Europa League group phase.
It was no less than Kane deserved after another fine display, and left his manager praising his attitude as well as ability.
"I have always believed in Harry since the first day," Pochettino said.
"That is football. I think it is possible to miss penalties, but it is not important.
"He found a way to score, to play and did not let it affect his performance. It was good.
"He showed character and personality. He has a very strong mind and Harry is a very good player, too."
Kane may well have been impacted by the lengthy wait he had before his penalty after AEL goalkeeper Karim Fegrouch sustained a nasty-looking blow to the head in taking down Kyle Naughton.
The Moroccan was taken to hospital with what Limassol manager Ivaylo Petev described as a "bad situation" and Pochettino was quick to send his best to the goalkeeper.
"Maybe it affected Harry," he said. "I hope the keeper is okay and makes a good, quick recovery."
Pochettino was delighted with his side's display, especially given he made nine changes from Sunday's 4-0 win against QPR.
Asked about Andros Townsend - called up by England despite being omitted from the squad to face the Hoops - Pochettino said: "It is good for him and other players that got 90 minutes and for the confidence.
"We have a lot of players, a very good squad and my job is just to choose the players for each squad.
"I am very happy, very pleased with the team. It was a very good performance today.
"There are no easy games because the Europa League is difficult to play, but we played very, very, very well against Limassol. We are very happy."
Pochettino said on the eve of the match that he had no intention in letting Townsend or Roberto Soldado leave before the end of the transfer window.
Sandro, Vlad Chiriches and Lewis Holtby are amongst the other players to have been linked with a move away but Pochettino remained coy on the chances of there being any movement before Monday's deadline.
"We have a lot of players with unbelievable quality," he said.
"We need balance and it is possible we add some players, but not too much movement before the end of the transfer window."