Brady, 20, has not played for Manchester United, but he showed glimpses of pure class at Craven Cottage, setting up two goals and scoring one himself.
Trapattoni hinted he could deploy the versatile United forward as part of a three-man front line in the Republic's next World Cup qualifier against Germany, but conceded his chances of playing will improve drastically if he plays regularly at Old Trafford or out on loan at an Championship club.
"I think Brady played well in the first half," said Trapattoni, who withdrew the winger after an hour.
"He scored a goal also and I think he can also do better.
"He might be called up in to the squad for the next match, but he would not necessarily be in the team (if he isn't playing regularly).
"This is a problem we have in our team, that five or six players only usually play 30 minutes or so every week."
The Republic put in one of the worst performances of Trapattoni's reign on Friday night as they scraped a 2-1 win in Kazakhstan thanks to last-gasp goals from Robbie Keane and Kevin Doyle.
Trapattoni made 10 changes to his team and the result was a much more fluent performance tonight, with Doyle, Shane Long, Seamus Coleman and Brady all impressing.
Trapattoni has often come under fire for being too conservative during his time as Republic boss, but his team threatened from all corners of the pitch and the Italian was happy with the performance of a number of his players.
"The victory is important for us," Trapattoni added.
"We made a lot of changes, but we played technically well. Brady was good, David Meyler played well and James McCarthy impressed me with his personality and so did Seamus Coleman."
Long put the Republic ahead when he nodded home a Brady free-kick from close range via the head of Sean St Ledger.
Brady then made it 2-0 with a sweet volley before Doyle nodded in a third from Brady's cross after 36 minutes.
Alex Pearce grabbed a fourth after Oman pulled one back through Eid Al-Farsi.
James McClean impressed when he came off the bench, just four days after he launched a scathing attack on Trapattoni's management skills in Kazakhstan on Twitter.
The Sunderland winger went close with two brilliant efforts, but his performance does not seem to have earned him a place in the XI for the qualifier against Germany on October 12.
"Probably no," Trapattoni replied when asked if McClean would start against the Germans in Dublin.
"Because I think about Aiden McGeady and others. Every manager must think about the strength of the opponents.
"I am not angry with him (about the Tweet). I never get angry with my players and I don't watch Twitter."
Trapattoni raised hopes that Simon Cox would be OK despite hobbling off with an ankle injury in added time.
"I think it's only a knock," Trapattoni said.
Oman boss Paul Le Guen launched a staunch defence of Trapattoni's management on Monday, insisting the Italian's career was far from finished.
The Frenchman was impressed with the performance of the Italian's team in south-west London on Tuesday night.
"It's not such a big surprise for me (how the Republic played)," the former Lyon and Rangers manager said.
"They are a powerful side, they are fast. It was too complicated for us and too many of our players are not fit enough because the season has not started yet in Oman and the players have just finished Ramadan. We knew it would be tough."
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