Robinson and England attack coach Brian Ashton were both at Lansdowne Road as Allen continued his rugby education during Gloucester's 37-20 Heineken Cup defeat against Leinster.
And Leinster skipper O'Driscoll, whose team's bonus point victory featured tries for Gordon D'Arcy, Stephen Keogh, Felipe Contepomi and Shane Horgan, praised another mature performance from the 20-year-old.
O'Driscoll said: "I thought Anthony Allen, in particular, looks a great prospect," said O'Driscoll.
"He is a very strong runner and there is no doubt he is a real prospect."
Allen and his fellow youthful Gloucester backs though, could not prevent Leinster leaving an immediate mark on Pool Two, despite first-half tries by midfield partner Jack Adams and wing Mark Foster.
"No side ever gets to the top without days like this one," said Gloucester head coach Dean Ryan.
"We need to take responsibility as a group, and we know what we have to do.
"I don't think we showed a lot of maturity, but I don't think that is very surprising because we have a young squad of players.
"The Heineken Cup doesn't allow you to make loose decisions without getting punished. We know we can score tries, but we just lost a bit of shape in the intensity of the match."
A fast and furious encounter also took its toll on the injury front, as Gloucester flanker Andy Hazell was forced off early in the second period with shoulder trouble, leaving him facing a fitness race for next Saturday's Pool Two clash against Kingsholm visitors Agen.
Ryan added: "Hazell is our main concern - he has got a bit of a 'stinger'."