Chelsea sacked Tuchel on Wednesday, a day after the London club suffered a shock 1-0 defeat at Dinamo Zagreb in their Champions League opener.
Tuchel led Chelsea to a third-place finish in the Premier League last season but they are sixth this term after six games, having lost away to Leeds United and Southampton.
"I was - it was right before the training session when we got the news,"
"It's always sad for any colleague in this profession to get fired. Unfortunately, we know how this works," Arteta said when asked if he was surprised at the decision.
"I wish him the best of luck. It's not pleasant to hear that news.
"... We have a profession that at some stage, this (can) happen. We have to prevent it, enjoy the journey and enjoy every day because you never know when that's coming."
Manchester United manager Erik ten Hag said he felt sorry for Tuchel, who led Chelsea to the Champions League in his first season.
Liverpool boss Jurgen Klopp said his club's owners, the Fenway Sports Group, have left it in his hands to get the team firing on all cylinders again.
"Obviously there are different kinds of owners. Our owners are rather calm and expect from me to sort the situation and not be thinking that somebody else would sort it," said Klopp.
"That is how they always saw it. And on the day when they changed their thoughts then they might tell me."
