Capello felt his side battled hard for victory in trying conditions, singling out Vincenzo Montella for particular praise.
He said: "It was a very good match, on a really difficult pitch. Both teams tried hard to win.
"Montella? His goal wasn't easy, but he's able to do these type of things."
Capello's Udinese counterpart Luciano Spaletti was disappointed his side slipped to defeat.
"It's a defeat that gives us pain," he said. "Now I have to evaluate what happened in the whole match.
"We made a few mistakes which Roma used to score, but these are things that are possible to improve on."
Roma's city rivals Lazio also had a bright advent to the campaign, notching a 4-1 win over Lecce.
Lazio chief Roberto Mancini was happy to kick-off the season with a win, but knows there is room for improvement.
"We are happy to have started with a win," he said. "Especially as we tired in the second-half.
"We need to improve our physical condition, but anyway it was a really fantastic first-half.
"In the next match, we will be in our best condition."
Internazionale ground out a 2-0 win over Modena, but the match was not without incident as sections of the Giuseppe Meazza crowd voiced their displeasure with the performance.
"We struggled until the end and it hasn't been easy," said goalscorer Marco Materazzi.
Inter coach Hector Cuper felt his side demonstrated improvement throughout the game.
He said: "We were slow in the first-half, but the second changed and we did some good things."
Brescia and Chievo kicked-off their campaign with a 1-1 draw, with both camps seemingly pleased not to lose.
Chievo chief Luigi Del Neri said: "The important thing is not losing. We are happy with what we did today.
"We are still thinking of salvation. As soon as it arrives, it will be better. After that, we will see."
Brescia coach Gianni De Biasi was happy with how his first game at the helm went.
He commented: "It is a big honour to take over the team of Mazzone; I'm convinced that in Brescia there is the chance to achieve big things.
"As for the match, it has been a good one. Probably we could have taken more."
