Pulis wants Middlesbrough centre back Ben Gibson, Everton midfielder Gareth Barry and Crystal Palace defender Joel Ward, while Barcelona centre half Thomas Vermaelen has also been linked with a move to West Brom.
West Brom were much the better side and made their dominance pay in the 31st minute as Chris Brunt swung a right-wing free-kick to the back post, where Hegazi rose to head through the legs of Begovic and in.
But even though Pulis' side won the match, the Welshman wants plenty more additions to his squad and cited the fact the club now have only 17 senior players.
"I believe that there's a tremendous talent pool in there and if that talent can not be realised immediately within our own ranks it is vital we get them out into league football to continue their development and education. Everyone around the club is waiting for them to come in".
"They have to be players that will improve us and we have to work hard over the next two weeks". The squad's just not strong enough. Squad is this, yes but we got 100% from the boys again.
Jay Rodriguez, another off-season arrival for the Baggies, had gone close on a couple of occasions prior to Hegazi's header, while Bournemouth looked uncharacteristically bereft of attacking verve in their quest for an equaliser. He's brought a lot of energy to the football club and it looks like he's going to score. We had really good opportunities and chances, we are not a possession team. "He's a good lad, speaks very good English, he's mixed in really well and he's done well alongside [Craig] Dawson today".