Although Morgan Stanley's analysts are separate from the underwriters, Morgan Stanley is one of the firms that took Snap public and priced the IPO.
"That was pretty much a seminal moment," Sorrell told CNBC's "Squawk Box" on Wednesday. Snap shares have languished below their $17 IPO price this week but rose slightly on Wednesday morning.
Facebook and fellow advertiser Google also face issues, Sorrell said. The pair has worked to prevent ads from being shown next to controversial and extremist content, and Google, especially, is still being pressured, according to Sorrell.
But he said that WPP's clients are still spending gobs more cash on Facebook and Google than on Snapchat.
Last year, WPP spent about $100 million on Snap, and Sorrell said that could grow to $200 million this year. But WPP's spending on Facebook was about $1.7 billion last year and will be "well over" $2 billion this year, Sorrell said. He added that WPP's spending on Google should grow from under $5 billion last year to between $5.5 billion and $6 billion this year.
"Snap obviously has been copied — plagiarized, you could say — by Facebook, and very successfully so," Sorrell said.
Paul Meeks, chief investment officer and portfolio manager at Sloy Dahl & Holst, said that Snap should have waited to go public since its business model was too immature and susceptible to copying by Facebook's Instagram app.
"I think Facebook is the one to buy, and if you think about Snap, slap yourself and just buy some more Facebook," Meeks said.
Snap and Facebook did not immediately respond to a request for comment.