Gleeson has been replaced by former Aston Villa manager Ward, who takes charge of her first game against Turkey on Friday before the trip to Slovenia on Tuesday.
Mannion said she was “really looking forward” to playing under Ward, who has a contract through to the end of the 2027 World Cup campaign.
“I’ve not played under her but I’ve spoken to her and she seems really excited, ambitious and hungry for the team to do well,” said Mannion.
“I’m sure she is keen to get us all in a room and tell us her visions and plans for the next number of years.”
The Republic will be without the experienced trio of Niamh Fahey, Diane Caldwell and Julie-Ann Russell, who all retired from international duty after the play-off defeat.
Mannion said they were “massive, massive characters who won’t ever be replaced”.
“Niamh Fahey and Diane Caldwell were massive role models as defenders and people for me, personally,” added the 29-year-old.
“Julie-Ann Russell had a year that nobody could have written, from when she first came into camp to where she ended up.
“It is so disappointing to see them step back and retire but I’m really thankful, on a personal level, that I’ve been on camps around them.”
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