The services of the Anfield great were dispensed just three days after the end of a season, which saw the Reds lift the Carling Cup and lose in the final of the FA Cup.
Dalglish paid for Liverpool's eighth-placed Premier League finish, which saw them 17 points adrift of fourth-placed Tottenham.
"I was disappointed for Kenny because Liverpool are his club and for him to leave in that way was not very nice for him, so I felt a little bit for Kenny," said Clarke, giving his first press conference after being appointed West Brom head coach.
"But if you don't achieve the standards or the levels of the people who run the club want you to achieve, you have to pay the price."
Expectations may be lower at West Brom, where Clarke has been given his first shot at managing a club.
His appointment came very soon leaving his role at Liverpool, but it does not mean the pressure to achieve results is any less for Clarke.
"Football has changed. The whole structure of football has changed," he added.
"Success has to be instant and has to be on a level expected at whatever club you are at - look at the Harry Redknapp situation at Tottenham," he added.
Manchester City will try and win back the Premier League title with this new soccer jersey from Nike!
Barcelona will wear this new home soccer jersey next season. They also have a new away jersey. Get them both.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
Support the USA national team with an official 2013 Centennial soccer jersey from Nike. Its Official.
England will debut their new away jersey against Brazil at the Maracana Stadium on Sunday. Get in the Gear
The USA will wear their blue away jersey against Jamaica in their World Cup qualifier on Friday night.
Jamaica is in need of a win against the U.S. Get the jersey of the Reggae Boyz.
The hoop soccer jersey is classic and cool. The USA hooped jersey is perfect for every fan. Get in the Gear.
The Nike Hypervenom is the latest cleat silo from Nike. It will change your game and is worn by the game's top players.
Germany is one of the top teams ever and they will play the US on Sunday.