Speaking after seeing his side snatch a dramatic point against Burnley through a 98th-minute equaliser by substitute debutant Brandon Thomas-Asante – signed from Salford City this week – the manager laid clear his emotions on a deadline day finale unlike any he had seen in his 25 years in management.
Fulham midfielder Onomah passed a medical and fulfilled media commitments at Albion's training base in Walsall but the club could not get the deal over the line, and it was the same in the case of Brighton's Colombia international Alzate, who underwent a medical in London ahead of the move.
Supporters voiced their anger after the significant disappointment at 11pm last night and chanted abuse aimed at principle owner Guochuan Lai against Burnley – but Thomas-Asante emerged from the bench late to salvage a priceless point that almost felt like three.
The manager said, however, that frustration and anger at not bringing Onomah and Alzate to The Hawthorns was palpable given the quality and difference they would've made to his squad.
It has been reported Albion were unable to complete and submit paperwork in time for Thursday night's deadline.
Bruce said Albion will hold an investigation into why the deals went awry and that the club must learn from any mistakes made.
"There will be an investigation into it, why? But I'm not going to go into details on that.
"It's really, really disappointing and frustrating because the two players would've been terrific acquisitions to the squad. For one reason or another we couldn't get it over the line.
"The frustration of everybody is absolutely huge, mad, disappointed.
"Josh Onomah was in the training ground and we still couldn't get it done. For the two players in particular it's a big disappointment for them.
"We'll have to learn from the mistakes we've made."
Bruce continued on the deadline: "I've said all along that we're in a transitional period. I've made some big calls and I've let players leave. Obviously when players leave, you want the replacements. We're devastated, disappointed, angry and frustrated about what happened yesterday.
"I'm not going to go into details because I don't think that'd be right, but it's angered everybody because we thought we had two very good players walking through the door. They've both played in the Premier League and they've both played very well.
"They'd have been terrific acquisitions. For them in particular I'm disappointed we couldn't get them over the line. It's all about the squad - we might be fortunate, it's been an unbelievable run of games in a quick period of time.
"We've now got eight or nine days. We've now got 14 games to play until the November break, so we have to channel it all there. We've got to catch a break with injuries, because we've got two big ones at the moment.
"There's nothing you can do about that, that happens. We are thin on numbers, for sure, but we thought we had three through the door, but we ended up getting the one."
The Baggies boss, whose side climbed a place in the Championship to 13th with the last-gasp point, added: "Yes (things can still surprise) – I've never known anything like that – not in the 25 years I've been going.
"As I said it disappointed everybody concerned, frustrated, angry, the whole thing came out for everybody.
"I don't think I want to go into all of that, because that would be wrong, there's too much (wrong)."
Bruce confirmed he started Thursday confident of seeing the new arrivals check into The Hawthorns.