He is now in line to break Giggs' record when the Baggies go to Arsenal on September 25.
"I think if you speak to the supporters who have supported the clubs Gareth has played for, they will always tell you that he has been an outstanding performer for them - and a consistent performer", said Pulis.
"Naturally I'm very proud to achieve those things today but hopefully I can keep clocking up the games for a while yet".
"To be fair, we looked to get more and that was three points and you have to say the quality in the last third was missing, either with a cross or a reaction from a cross or something, or when we had good one-on-ones in the last 20 minutes, when they opened a little bit".
"It's nice for my family and something to make them proud". It's one of those for a few years down the line yet, once I've finished playing and I can look back on it all - while I'm resting some exhausted legs.
"It's game by game, season by season, but I think there's some gas in the tank yet!" You stop when you stop enjoying it and I'll know when I've had enough and can't keep up with the boys.
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He said, "West Brom were poor against Brighton, it was like they thought they would just turn up and not lose, but they were bad until they went 3-0 down, then they had a go".
He added: "He was a player I admired and respected, when we brought him into the club we realised how good he was".
"He's like Fletch (Darren Fletcher) in lots of ways. We're pleased to have him and it's a privilege to work with him".
He also won the Premier League with Manchester City in 2012 and earned 53 England caps.
632 - the appearance record he now shares with Giggs.
West Ham remain in the bottom three after five games but there were at least more shoots of recovery for the visitors at The Hawthorns on Saturday.
21 - seasons in the top flight for Barry.