The former Liverpool defender has asked why Arsene Wenger didn't sign Costa when 'everyone knew Arsenal needed a proven striker,' while also questioning whether £35 million man Sanchez was really what the Gunners needed.
Interestingly, though, Carragher did not stop there.
Indeed, the Sky Sports pundit feels Wenger should have signed Filipe Luis to address Arsenal's left-back position, as well as goalkeeper Petr Cech.
"Why wasn’t Wenger in the market for Costa when everyone knew Arsenal needed a proven striker?" Carragher pondered in his column for the Daily Mail.
"Why not try to sign Petr Cech, the best goalkeeper in the Premier League last year? Yes, Alexis Sanchez has quality but was he really what Arsenal required?
"I’ve said before that Arsenal’s spine is not strong enough. With questions hanging over Nacho Monreal and Kieran Gibbs, they needed a left back, so why didn’t they rival Chelsea for Filipe Luis?"
The Gunners travel to Aston Villa later today, having lost 2-0 at Borussia Dortmund during midweek.
Last weekend, Wenger's men drew 2-2 with Manchester City at the Emirates Stadium, with goals from Jack Wilshere and Sanchez securing the point.