Late on in their 2-1 defeat against Birmingham, Beale opted to substitute the right-back in the hopes of salvaging a result.
Footage shows Hume doing the common practice of stretching out his arm for a handshake from his manager as he made his way to the bench.
However, Beale appeared to ignore him and Sunderland fans on social media were left displeased with how the 43-year-old acted.
The Black Cats boss was asked about the alleged snub afterwards and revealed that it wasn't a deliberate act.
Speaking to BBC Radio Newcastle about the incident, Beale said: "I didn't see him, to be honest.
READ MORE CHAMPIONSHIP NEWS
West Brom boss sent off for moment of madness just six minutes into Southampton clash
'I'm going to cry' - West Brom fans rejoice as takeover saves club from financial abyss
"Trai passed a fitness test to play today and he was on a booking, so it was easier to keep Leo on when we made the change.
"If I've missed him, I'll have to go and see him now and say that to him. Listen, he is probably as close to me as any other player in the squad.
"There was nothing there between me and him, I honestly didn't see him."
Beale then took to Instagram to add further clarity, saying: "Trai Hume is a fantastic player for our club. He gives everything for his teammates and the staff.
Most read in Championship
Phillips 'can't go to the Euros' as West Ham move goes from bad to worse
Nottingham Forest create bizarre new role and appoint former referee Mark Clattenburg
Arsenal break Premier League club record with 13 games to spare as Gunners run riot again
Liverpool duo Jota and Jones leave in protective gear but Klopp has positive Nunez update
"I wasn't aware that I missed his handshake until being asked about it post game. I immediately went to see him to apologise.
"Trai passed a fitness test this morning to play the game and I cannot hold him in higher regard as a man or professional.
Sunderland legend Kevin Phillips stunned by club's welcome decorations for Newcastle fans at Stadium of Light ahead of Tyne-Wear derby
"He is an example of everything that is good about a young footballer and our team."
Sunderland's defeat at St Andrew's was their 14th loss in the Championship, with the Wearside outfit now suffering back-to-back defeats.
Beale, formerly of Queens Park Rangers and Rangers, replaced Tony Mowbray as Sunderland manager in December.
But it was Mowbray that got the better of him on Saturday as goals from Jordan James and Koji Miyoshi sealed the win for the Blues.
Jack Clarke opened the scoring for Sunderland, however they failed to take at least a point back to the Stadium of Light.
The result means that Beale, who has come under increasing pressure from fans, has won just four out of his 12 games in charge.
Sunderland now sit tenth in the Championship and four points off the play-offs as they continue to eye a return to the Premier League.