Just over six months after being appointed to the job, Irvine was fired by the club on Monday following a run of seven defeats in nine Premier League matches.
That sequence saw West Brom drop to 16th in the table, just one point above the drop zone.
Irvine's exit marked the third managerial change at The Hawthorns in 12 months, after Steve Clarke departed last December to be replaced by Pepe Mel, who subsequently left at the end of the 2013-14 campaign.
With a visit to West Ham looming on Thursday, Kelly says the players and staff at the club have to prepare for the game as best they can.
"I got a phone call last night from Alan explaining the situation," he said in a press conference on Tuesday.
"Terry [Burton, West Brom's technical director] then rang me, and told me to prepare the team, along with Keith [Downing] and Dean [Kiely] as best we can for the upcoming fixture against West Ham.
"I am disappointed but I know Alan would want us to carry on and get on with our work. It is exactly what he would want, so that is what we will do.
"I spoke to him briefly but I think he had other things to do. We will talk properly when the time is right."
Kelly was fulsome in his praise of Irvine, and said he felt the players would be disappointed about the Scot's departure.
"You would have to ask them but I'm sure they were, they have got a lot of respect for Alan," he said.
"He's a terrific person, first and foremost, a terrific man, and an excellent coach.
"They were told by Terry but they knew anyway, because they had seen it on television and local media, so it was not a shock or a surprise. I think they had got over that.
"They came into work, it is what we do. We are professional people, so we get on with our jobs, which is exactly what Alan would want us to do.
"We will prepare as best we can to go and get a result against West Ham."
