The Italian says the club did not want to stand in the way of the Spaniard, revealed Cristiano Ronaldo will be rested this weekend and remained vague on last-minute transfers.
The Spaniard joined up with Pep Guardiola at the Allianz Arena, filling the void left by Toni Kroos who had gone in the opposite direction earlier in the summer.
Ancelotti admitted that the 32-year-old's transfer request was unexpected - and unwanted - but that he could understand Alonso's wishes to try out life away from the Santiago Bernabeu after five years with the club.
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"Everybody at the club talked to Xabi about it," he told reporters on Saturday. "He explained it well. He said he needed another motivation. Clearly it was a surprise. It was all quiet here, but Xabi decided to go. We were surprised but, as I said, we respect him a lot. He was very honest with the club.
"All Madrid fans and players see him leave in high regard. It was very difficult to change his mind. Considering what Xabi has done for the club, you cannot just say: 'No, you can not go'. I wish him luck, I think he was a very important player last year for us to win the Champions League and Copa del Rey.
"However, we are in a very good position anyway because we have Asier Illarramendi and Toni Kroos who can be useful in that position this season."
Real Madrid travels to Real Sociedad on Sunday but will be without UEFA's newly crowned Best Player of the Year, Cristiano Ronaldo, as the Italian confirmed he is being rested this weekend and throughout the international break.
"Ronaldo's fitness is generally good, but we have chosen this week to get him back to optimal condition in preparation for the match against Atletico Madrid and Champions League games," Ancelotti added. "Tomorrow Ronaldo will not be part of Real Madrid's squad."
Ancelotti admitted the club remains open to more signings, with reports suggesting a move for Monaco striker Falcao is imminent.
"I cannot confirm anything transfer wise," he continued. "The market closes Monday - something may happen, something may not happen.
"We do not need any more players, but we have a squad template which offers flexibility. Until the market closes, we cannot say whether we will sign anyone."