Leicester lost 2-1 on Sunday to the Sky Bet League Two minnows - 74 places below the Foxes in the football pyramid - after Puel had made seven changes from the New Year's Day win at Everton.
England internationals Jamie Vardy, Harry Maguire and Ben Chilwell all missed the third-round tie at Rodney Parade, as did goalkeeper Kasper Schmeichel, full-back Ricardo Pereira and midfielders Wilfred Ndidi and Nampalys Mendy.
"I do think any criticism (of Puel) would be unfair," Leicester captain Morgan said after Newport claimed their first top-flight scalp in the FA Cup for 55 years.
"Obviously people will look at the result and judge by that. But if you look at the chances and opportunities we had, we could have won that game quite easily.
"We've got a good squad and the gaffer's got the problem of finding the right balance. He's got to give players rest and other players opportunities.
"It's the same for every manager and every team - and I thought we were definitely strong enough."
Leicester supporters, however, were clearly not impressed with Puel as the 57-year-old was roundly jeered as he passed the end housing them to conduct his post-match media duties.
The former Southampton boss has come under pressure in recent weeks, despite festive wins against Chelsea, Manchester City and Everton taking Leicester up to seventh in the Premier League.
Puel was sharply criticised for naming an under-strength side for the Carabao Cup quarter-final defeat to makeshift Manchester City opponents last month.
Foxes fans felt the club had passed up a presentable chance of winning silverware, and history repeated itself in south Wales as Padraig Amond's late penalty saw the 2016 Premier League champions become the biggest third-round casualties.
"It was a difficult day and the magic of the FA Cup happened, definitely," Morgan said.
"I felt we played well, especially in the second half.
"We had loads of half-chances, some very good positions where we should score, and on another day they all go in.
"But it didn't happen for us and we're very disappointed to go out of the competition.
"I wouldn't say they deserved it, but I don't want to take the shine away from Newport.
"It's a big day for Newport and good luck to them."
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies