The midfielder, who made a return from injury last month after about a year on the sidelines, was a notable presence in coach Igor Tudor's starting XI. His comeback was un unhappy one as they succumbed to a 2-0 away loss at Stadio Olimpico.
It was the 28-year-old's second game of the season following a substitute appearance against Genoa last month. He was withdrawn from Wednesday's game in the 58th minute.
"I am very happy to be back on the field," Udinews TV.
"I have been here for almost nine years and the affection I feel in Udine is very important for me, with a great company and incredible fans.
"But I'm not happy with the result.
"We played against a very strong team, we did better in the second half but with the rigour and the episodes it went wrong."
Udinese's struggles this season have left them occupying the 18th position, two places and three points above the relegation zone.
"We must forget everything immediately because in two days there is a very important match," Badu added.
"We should immediately think of Sassuolo on Saturday afternoon, it will be a war and we must try to win. For us they [remaining matches] are now all final."
Badu, who has played at five Africa Cup of Nations tournaments as well as the 2014 Fifa World Cup, will be hoping to mount a late fight for a place in Ghana's squad for the upcoming continental championship in Egypt.
He recently revealed, though, that he does not believe he is in coach James Kwesi Appiah's plans for the tournament.