The Foxes are set to host Southampton on Tuesday night for the fourth round tie postponed in the wake of the helicopter crash which killed Srivaddhanaprabha and four others following the Premier League match against West Ham on 27 October.
Puel said ahead of Saturday's 1-1 draw at Brighton it was time to try to move forward following the tragedy and focus on football as the players returned to domestic action after the international break.
The French coach guided Southampton to the 2017 EFL Cup final where they lost 3-2 at Wembley against Manchester United.
Puel believes another timely cup run would help heal the emotional wounds of everyone connected with Leicester and their charismatic late owner.
"It's important to play all these games with the right desire and good aggressiveness and mentality. We have the squad to maintain a good level," said Puel, who will be without England defender Harry Maguire, while midfielder James Maddison will serve a one-match suspension.
"It will be a good opportunity for the squad to perform together and to win something. We know the importance of winning something. The cup will be important for us.
"The chairman liked it a lot and it will be our desire to try to perform. We know the difficulties in the cup, but it's a good motivation."
Puel believes Leicester have made solid progress, but remain in need of a cutting edge following three draws from the past four Premier League games.
He said: "We need to continue to improve our quality in the final third. We continue to improve young players, step by step, some find themselves in the national team for the first time.
"It's a good mix of youth and experience and we have to perform and want to finish in the top half of the table, as high as possible. Afterwards, we have to look at looking something with the cups."
Puel accepts the poignancy of the occasion on Tuesday night, as Leicester play another home game at the venue Srivaddhanaprabha had come to feel his own.
"Before we had a good togetherness, but of course after an event (like this) we have more focus. More concentration on the objective," he said.
"It's a common aim. The most important thing is to play together, to perform and to pay tribute to our chairman at the end.
"It's our responsibility and I hope we can have this in our head all the time."
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