The Hungarian told BBC Radio Suffolk: "He's a good goalkeeper. Arran's a great professional.
"I came here and Murph was on the bench in front of him, he really deserves his promotion because he was training really hard."
Irishman Murphy is expected to be sidelined for three months after undergoing surgery on a broken ankle on Thursday.
The 27-year-old replaced Lee-Barrett as boss Roy Keane's preferred option between the sticks shortly after his arrival in January.
When I first came here our first four or five games we were unbeaten and I was even thinking about automatic promotion
Ipswich Town goalkeeper Marton Fulop
But Fulop's transfer to Portman Road from Sunderland in the summer saw him supersede the pair in the Town starting line-up.
And with 18 games to his name this season, Fulop thinks he has seen enough from his team-mates to believe they will improve on their position of 18th in the Championship.
"If you lose a lot of games on the trot, you can win a lot of games on the trot, the Championship is like that," the 27-year-old said.
"If you can get three of four wins it can get you to where you want to be.
"When I first came here our first four or five games we were unbeaten and I was even thinking about automatic promotion.
"But it's nearly the same squad as it was before so I can't see why we can't start winning again."
Source: BBC Sport
Source: BBC Sport