The Baggies pulled the plug on Pulis's time in the hotseat on Monday after a torrid run of form that had seen the club collect just two wins from their previous 21 Premier League games, leaving them on the brink of the relegation zone.
Pochettino's side welcome West Brom to Wembley this Saturday and speaking in his pre-match press conference today, he admitted that he was upset to see Pulis lose his job.
"Nothing surprises me. I feel sorry for him, we have a good relationship, always when this happens in football it's painful," he said.
"You prepare [for the game] with all the information under Pulis, but it's true, maybe they can change in a week. We are not going to have information if they are going to change their shape. It's difficult.
"We struggle a little bit with opponents who come to Wembley and play deeper. We need to improve in our position game in the final third. We need to show more patience to build chances. It's a thing we need to improve.
"West Brom is a team that is aggressive, physically strong. We are going to be ready to fight because it is a team that loves to counter attack, works very hard in set pieces. We need to try to avoid this type of situation."
Spurs won the equivalent fixture 4-0 last season, with Harry Kane grabbing a hat-trick.