The 19-year-old left-back was playing in the biggest match of his young career on Tuesday night, only for an unfortunate slip to present Manchester United midfielder Park Ji-Sung with an early away goal.
But captain Fabregas has every confidence Gibbs can shake off this disappointment, claiming: "Kieran has been amazing for us. He is a very strong guy and he will be a great player for Arsenal and England."
Before Arsenal could regroup from the nightmare start, Cristiano Ronaldo drilled in an audacious 40-yard free-kick past Manuel Almunia to make it 3-0 on aggregate and effectively kill off the tie as a contest inside 11 minutes.
Gibbs, who came through the Wimbledon academy before joining Arsenal, has been thrust into the Gunners' starting XI following a back injury to Gael Clichy, but was withdrawn at half-time last night by manager Arsene Wenger.
"Kieran has been so unlucky (against United)," Fabregas added. "He was devastated at half-time, and that made me really sad because he is only 19 and this can happen to anyone."
Arsenal now have little more than pride left to play for - although an unbeaten run of 21 Barclays Premier League run has given them an outside chance of overhauling Chelsea, whom they host on Sunday, for third place.
Fabregas accepts the Gunners must do better if they are to fulfil their undoubted potential.
"It has been a difficult season, for a young squad like ours we did quite well," said the Spain Euro 2008 winner, who missed a large chunk of the campaign because of a knee problem.
"We worked hard and were also in the FA Cup semi-final, playing against great teams, but we still have to improve a lot for next season. It is tough, but you have to stand up and look for the future."