Gibbs, who scored for the first time ever in Europe, believes their display was the perfect riposte to fierce criticism that followed last weekend's defeat to Aston Villa.
"The performance was needed after the start of the season and to prove to ourselves and everyone what we are capable of," he said. "It was a solid performance and to be honest and I think it was better in the first half than the second. We deserved to score in the first half but we became more clinical in the second which was important as it got us the away goals.
"The manager believes in us and we believe in him so we felt we had a point to prove to him and the fans. We've done that and now it is just about getting on with this season and we are determined to get results like tonight.
"We have dealt with pressure in the past couple of seasons - before the Bayern game and after the Milan away game - and the players stepped up tonight and showed what they are made of and showed what we are looking to produce this season."
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