The Argentine was axed this week after just a year in charge despite steering Chelsea to a sixth-place finish and Europe next season - three points clear of Newcastle in seventh.
"Very surprised," Howe said in Melbourne after winning a post-season friendly against Pochettino's former club Tottenham on Wednesday evening.
"I think Mauricio is a very, very good manager, he's done incredibly well regardless of the club he has managed in various countries.
"I think it's sad for the Premier League when a manager loses his job," he added.
"Especially when I think it is harsh as his performances have been very strong."
Some reports in England have said the highly-regarded Howe could be in the running for the Chelsea job.
Although Pochettino led the Blues into Europe after a strong finish to the campaign, it was a difficult year for the former Spurs and Paris Saint-Germain boss.
His side were booed by their fans after several dismal performances and lost the League Cup final to a youthful Liverpool side, as well as suffering an FA Cup semi-final defeat against Manchester City.
But Howe thought he was doing "a really good job".
"The latter part of their season their form was very strong, they pipped us for sixth place," he said.
Pochettino is the third manager after Thomas Tuchel and Graham Potter to be axed since United States-based Todd Boehly's consortium bought Chelsea.
Newcastle have one more friendly to end their season, against an A-League All Stars side on Friday, again in Melbourne.