The Potters' highest profile signing this summer has been the £8million capture of striker Kenwyne Jones from Sunderland.
But Jones suffered an ankle injury during the 2-1 loss against Wolves on Saturday, marring what had been a promising debut.
Shawcross is certain Jones will prove a success at the club and is hopeful the Trinidad & Tobago international will be joined by further new faces at Stoke.
He told The Sentinel: "Kenwyne was one of the toughest strikers I faced last year, so he is going to be a challenge for any centre-half.
"He will suit us and the style we play and might add that bit of quality.
"If we can bring a few more players in, that might add more quality as well.
"The manager has stated we need a couple just to lift the squad. Hopefully, we will get some in this week."