Keane came off the bench as a half-time substitute and helped himself to his 55th and 56th goals for Ireland as the Republic romped to a 4-0 victory over the 10-man Georgians who laboured after keeper Giorgi Loria's 20th-minute dismissal.
Derby defender Richard Keogh had opened the scoring three minutes before the break with his first senior international goal, and Nottingham Forest striker Simon Cox extended the home side's lead three minutes after the restart before Keane sealed the win.
"Robbie was destined. He started to play as an 18-year-old and was one of the youngest creative players in Ireland," Trappotoni said.
"He has played in famous teams in Italy and Tottenham in England, and he continues to show us his creative quality.There are players who feel goals, and Robbie is one of these players. He has shown us he is not finished because also in Los Angeles, every week he scores goals.
"There are strikers who have a particular feeling for goals and Robbie is one of these. He will be a great for Ireland because in the future he will continue and in the next game, he will have the most caps."
Keane will overtake keeper Shay Given if, as expected, he leads Ireland into their World Cup qualifier against the Faroe Islands at the Aviva Stadium on Friday evening, and he admits that is not something he ever envisaged.
"If you had asked me 10 years ago if I would get this many caps, I would have said you were crazy," the LA Galaxy frontman said.
"Obviously I am delighted and I am sure I will look back in years to come on it - but hopefully I will get a few more yet."
Keane's contribution put the icing on the cake for the Republic, who were 1-0 ahead when he arrived.
Keane struck for the first time 13 minutes from time when he tapped home substitute Conor Sammon's low cross, and he converted Jeff Hendrick's 87th-minute pass to complete a comfortable win.
"Obviously, we are happy with the result. I said this morning to the team not to under-evaluate Georgia after the result in England," Trappatoni said.
"We could not under-evaluate Georgia. In fact, we started a little bit nervous and in the first 10 minutes, we missed some passes.
"With some beautiful offensive play, Shane Long could have scored a goal and the goalkeeper made this mistake and that helped us because with 10 against 11, we had more facility to achieve a result.
"But after that moment, we increased our personality. Yesterday, I said it would be important to see how this one man, James McCarthy, improved and also today, James played very, very, very well.
"I gave him my congratulations because he played with personality and saw the play, and he can grow again much, as can the others.
"This result is good for the future, it gives us a more concrete facility to think we are an important team and a team that can achieve."
There was an important cameo, too, for defender Richard Dunne, who played the last 15 minutes on his comeback from a year-long absence through injury.
Asked afterwards if he was in contention to start against the Faroes, Trapattoni said: "Yes. It was a good enough performance."
Dunne was delighted simply to have been involved after a nightmare 12 months.
"Ideally, you would try to play games behind closed doors and stuff like that, but as games go, I don't think it could have gone more perfectly than today," Dunne said.
"It was ideal. It was what I wanted, just the confidence to know that I can compete and more so, the week's training has been as hard as the game was today.
"It was important for me just to clear my mind of what has gone on in the last year, and I feel now that I can progress and play again for a couple of years."