Cox has only started two games for his club, both in the Carling Cup, and did score against Bournemouth. He has just two substitute appearances to his name.
Hodgson revealed the fourth striker in Trapattoni’s squad, who is keeping out Newcastle’s in-form Leon Best, came close to a third at Sunderland.
He said: "I have a relationship with Giovanni and where he was exceptionally good was in transfer deadline week.
"It took a long while to get the Long transfer through and he had actually joined up with the Ireland squad but Giovanni was very good and let him spend the day with us and complete his medical.
"It suits Ireland to have him playing in the Premier League and with Doyle, Long and Keane and Cox as well. They look strong.
"Simon was in good form and was unlucky not to get on today and under normal circumstances I would have put him on with Peter not at his best but I didn't want to destroy Peter and was hoping he would produce a bit of magic late in the game. But I was wrong on that one."