The pair came together on Monday, with experienced midfielder Morrison apologising for hitting young striker Berahino after the 20-year-old reportedly refused to say sorry for a mistake that led to Cardiff's late equaliser in last Saturday's 3-3 stalemate.
West Brom have sought to play down the incident over the week and Mel was keen to present a united front ahead of the final seven games of the season.
The Baggies boss said: "They solved the situation between themselves in a perfectly natural manner almost as if they were two brothers from the same family.
"I spoke to Saido - he perhaps seems to be more responsible than other people of his age and I told him that I trust him and trust that he will continue to work well."
It is understood the club have no intention of selling Berahino, who signed a lucrative new contract in December tying him to Albion until 2017, although they declined to confirm whether either player had faced disciplinary action.
Mel insisted he would have no second thoughts about selecting Berahino for the remainder of the season, including Saturday's trip to Norwich.
The Spaniard said: "I've been impressed with Saido, he's worked very well this week.
"In addition to being an excellent player, he is also intelligent. He has shown this in training. And I'm sure he will continue to show this.
"I've spoken to him throughout the week. He is very positive. He will be important to us in the final seven games."
Mel did not want to elaborate on what happened in the dressing room at The Hawthorns, saying only: "Eighteen young sports players have come in disappointed.
"It's normal they would argue among themselves. After that it's normal to have a beer and forget about it. The players were disappointed they hadn't won the game for the supporters.
"I prefer to have players who are cross when they don't win rather than players who go home to watch television and are perfectly fine with that."
One thing Mel was disappointed about was that the incident had found its way into the public domain.
He said: "The dressing room is the home environment. If any news gets out, that is bad news for us. What happens in the dressing room, should stay in the dressing room. I hope we have a positive reaction from this at Norwich."
Mel's efforts to move on from the incident have not been helped by Berahino himself.
The forward was reported to be considering legal action against Morrison, which prompted West Brom to issue a statement on Wednesday evening with a quote from Berahino saying he would not be suing.
But on Thursday he posted a cryptic message on Twitter with a quote from the Bible, saying: "A patient man has great understanding, but a quick-tempered man displays folly."
The tweet was subsequently deleted.
Former West Brom striker Peter Odemwingie weighed into the debate, saying Berahino should learn from his experience and leave West Brom.
Odemwingie had a high-profile and bitter falling-out with the Baggies in January 2013 after failing to push through a move to QPR.
The striker eventually left the Hawthorns last summer for Cardiff before moving on again to Stoke this January.
Odemwingie wrote on Twitter: "I see a repeat of my situation if he doesn't leave this summer. Senior pros haha."
The tweet was 'favourited' by Berahino.
Mel was not willing to enter into debate about Berahino's Twitter activity, saying: "Communication on Twitter is very cold. I believe in him as a player and I believe we have players who are committed for the rest of this season."