Saul had a difficult debut against Aston Villa, which saw him replaced at half-time by Jorginho, but Azpilicueta feels his fellow Spaniard just needs time to adapt having never played outside his homeland before.
Before their Champions League win against Zenit St Petersburg, Azpilicueta said: "Saul is a great player, I know him from his time in the national team. He has great experience at the highest level with Atletico Madrid in the Champions League.
"When he signed for Chelsea he had a bit of a stressful last few hours of the transfer window, he arrived in a new country, had just a few training sessions before his first game against a good opposition who were very aggressive.
"So it's normal, sometimes you need a bit more time to adapt and his response has been absolutely spot on, his desire to improve, asking questions, he wants to adapt as quick as possible. He has our full support, he's a great addition, I'm very happy to have him in our team. I'm sure that he will keep growing and helping the team because we need everybody and I'm sure that he will be an important player in the season."
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