The Republic's football team suffered disappointment in their first Euro 2012 match, losing 3-1 to Croatia.
Earlier, President Michael D Higgins had called on the Ireland team to do what is necessary in Euro 2012 and said he was hopeful of good results.
Before the match, the President was mobbed by a 20-strong crowd from west Belfast outside the squad's hotel in Poznan.
The President, a lifelong Galway United supporter and the club president, was presented with an Ireland jersey by manager Giovanni Trapattoni ahead of the game in the Miejski stadium.
The President opted not to take the Government jet to Poland and flew into Poznan on a commercial flight alongside several hundred Irish fans who sang most of the way.
One of the fans who met the President, Michael Hughes from Ladybrook in Belfast also met Trapattoni at the hotel.
"I saw Marco Tardelli first and then I saw Trap and I went up and said 'I love you'," he said.