Fousseni Diabate also scored twice on a promising debut, with Wilfred Ndidi completing the scoresheet.
'I used my own opinion but my son knows Fouss very well and he gave me good news about him and his positive, professional attitude.
'Who have I been linked with today?
"We set a target and we hit it but there is loads and loads of talent out there", he said. The cup journey is a good reward for all the team.
"It's a lovely competition to play in".
The Nigeria global then doubled his tally by steering in a volley from Christian Fuchs' sensational left-wing cross after 29 minutes.
Though, Leicester City will be hoping to do all they can to keep hold of the player who is the spearhead of their attack.
Prior to that the Nigerian worldwide who appears to have adopted "operation convert every chance that comes your way" as a slogan, narrowly missed scoring the third goal, but his two goals brings his total to nine in nine FA Cup appearances.
And his boss who is pleased with the "good mix" between experienced and young players sees the former Manchester City forward doing great things with the King Power Stadium outfit in future - while reserving special praise for debutant Fousseni Diabate.
"No one knew of him", Puel added.
Peterborough may have sensed a cup upset following Puel's decision to rest a number of key players ahead of their Premier League clash at Everton on Wednesday night.
Iheanacho collected the ball from outside the area and arrowed a fine left-footed strike into the bottom-left corner to double the Foxes' lead, and he made it 3-0 on 29 minutes by steering in a volley from Christian Fuchs' sensational left-wing cross.
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