Fr Wallace, who took his own life on Friday, was laid to rest on Tuesday, after 40 years of service in Turf Lodge.
The 69-year-old's death has shocked local residents and members of the church.
At his funeral in Holy Trinity Church, fellow priest Fr Thomas McGlynn described him as an "incredible man... an incredible priest".
Fr McGlynn also spoke of the increasing demands placed on priests, adding that Fr Matt had become "weakened and dispirited".
At Requiem Mass, Fr McGlynn spoke of how priests were facing "burn out" because of the "difficulties of contemporary priestly life" in a "bruised and wounded" church.
Father Matt really put his heart and soul into it. In many ways, he put his heart and soul into everything.
Fr Martin Magill
The priest's death came as a shock to the community, and for many there was a sense of disbelief surrounding his death. However, Father Martin Magill said he understood the comments made at his funeral.
Fr Magill said: "Without any shadow of a doubt and I would guess most priests would agree it certainly has complicated things.
"I think the bad publicity and the ongoing publicity, not handled very well at times by the Catholic church, which would have contributed to that as well.
"There's a lot of anger, understandably so, which has added to it," he added.
Fr Magill explained: "There are times when we as priests are also hurting, hurting on a number of levels.
"Hurting as we hear some of the horrific things that have been done to children by some of our priests, by other people, maybe people know."
In recent months, a pilot group known as Well Being has been set up to help clergy of all denominations to deal with issues affecting them.
Rev Lesley Carroll, of Fortwilliam and Macrory Presbyterian Church, has been involved in the start-up.
She told UTV it has been an invaluable experience for her, and others.
She said: "You don't feel as isolated. Often in ministry you feel very isolated, there's only me, there's only me dealing with all of this, and that's simply not true.
It exists because of the strains but it also exists because of the world in which we live and the changing situation and culture that the church sits.
"So when you go into a group experience you realised you're not alone, other people have been living like this and you glean learning from each other's experiences."
Phillip McTaggart, from suicide prevention charity PIPS, said the death of Fr Matt has had a devastating impact because of his role in the community.
He explained: "You normally think of just eh ordinary person on the street who will end their life in this sad way. But when it's a priest then it comes home that this really can happen to anyone."
It is hoped the Well Being scheme will become more widespread across Northern Ireland, giving members of the church somewhere to seek help and discuss issues affecting them.
Sue Ramsey, Stormont's health committee chair, has echoed calls for provisions to be made available for those who give aide to the public.
"A lot of people knew Father Matt," she said, "he actually got on with a lot of people in my constituency and a lot of people went to him with their own troubles.
"It's important that people do get the help and support that they need, especially those who are in a professional capacity taking on other people's issues.
Samaritans telephone: 08457 90 90 90
She added: "This issue about Father Matt sadly taking his own life has sent out a sad message that everybody needs to have that space to get the support so that they can help others."