The 27-year-old, a £5million January signing from Swansea, is yet to find the back of the net in eight appearances for his new club, and with leading scorer Steven Fletcher ruled out for the rest of the campaign, he is the only frontman with Barclays Premier League experience at the Italian's disposal.
However, Di Canio saw enough in Graham's individual display in Sunday's 3-0 derby victory at Newcastle, during which he was denied what looked likely to be a certain goal when he was hauled back by Steven Taylor in an incident which was missed by referee Howard Webb, to believe he will play a key role during the remaining five games of the campaign.
Asked if Graham's personal drought had affected his confidence, the 44-year-old said: "It can happen, but to him it didn't happen because I have seen him really focussed and in a good mood.
"That proved that even if sometimes strikers are selfish - they have to be selfish sometimes, but not too much, because when they are in front of the goal, I don't want to see tippy-tappy, I want see them strike and destroy the goal.
"But the fact that he is in a good mood, he has proved to me that he is intelligent, that first of all, it's the team.
"We won, we won in style. He feels the cause and he is full of confidence. I'm sure it doesn't affect him that he hasn't scored since he came here because he is sure now.
"Sometimes people don't understand - strikers have to score goals. But sometimes they are crucial even if they don't touch one ball, in my opinion, and Graham did this job and was amazing.
"But I am sure that before the end of the season, he is also going to score important goals."
That Graham was not needed to register for the first time at St James' Park was testament to the efforts of Stephane Sessegnon, Adam Johnson and David Vaughan, who all scored from distance as the Black Cats cut loose.
Johnson's sumptuous strike was particularly welcome as a desperately difficult first season since his £10million summer switch from Manchester City entered its final few weeks.
The 25-year-old has struggled to reproduce his best form on a consistent basis, but Di Canio was delighted with his contribution and is confident there is more to come.
He said: "He has very good quality and we have to put him in a position to use his talent, his quality, and then to can be easier for him to express the talent he has got.
"It's clear what he did on Sunday on the ball, but also off the ball he has started to improve.
"He was another guy with Stephane who, previously when I watched a few Sunderland matches, once they lost the ball, they used to say, 'I don't care now, you try to work for me'.
"It was not because they are bad professionals or because the are bad guys, but probably because they had the chance to do this.
"That is a mutual exchange - we play in an 11. We are footballers, we play as a team, so thanks to them - but that should be normal for us."
Amid all the euphoria of a famous day on Tyneside, no-one within the Sunderland camp is losing sight of the fact that the club is still fully engaged in a battle for top-flight survival, or that defeat by Champions League-chasing Everton at the Stadium of Light on Saturday could undo much of the good work.
The Black Cats have not beaten the Toffees in 19 attempts in all competitions, 16 of them in the league, since December 2001.
Di Canio said: "I love, I have to be honest, the way they [Everton] play because there is a clear identity from the manager. The only problem is how to damage them.
"We have done the right things in the last few days and we are ready to try to get the best result we can."