Xabi was sacked by Real Madrid two days after the Spanish Super Cup final defeat to Barcelona in Jeddah, Saudi Arabia.
Guti told DAZN: "I didn't experience the daily life of what the dressing room was like with Xabi Alonso.
"At the same time, it's true that when a dressing room isn't comfortable, isn't happy with the coach, it shows and it's very noticeable not only in training, but also in matches. I think this was the trigger for Xabi's dismissal at this time.
He then added: "I don't think it's due so much to his style of play, or what he did on the pitch. Earlier I was looking at a statistic that (Hansi) Flick, the Barcelona coach, had the same results as Xabi Alonso in his first 34 games. That means the way the matches went wasn't bad. But it's true that there were a lot of rumours that he couldn't adapt because of the dressing room."
On Alvaro Arbeloa, who steps up from his Castilla post to replace Xabi, Guti said: "He's an unknown quantity, but when Zidane arrived, he was too. Looking at Real Madrid Castilla, things weren't going well.
"Whether he's ready or not, Madrid will know because he's been working in the youth academy for a long time, and if they've given him this responsibility, it's because they believe in him and are now waiting for things to go well."