City have endured a stuttering season so far, unable to find any real consistency with injuries to key players like captain Vincent Kompany and Sergio Aguero not helping.
As a result of City's failure to convince in the title race, speculation has been rife over the future of Pellegrini with rumours abound that Bayern Munich boss Pep Guardiola is set to replace him at the Etihad helm, as reported by the likes of the Mirror.
That pressure would have increased had it not been for late goals from Yaya Toure and Aguero as City turned things around in style.
'Man City constantly worry me'
But BBC pundit Shearer, who scored 313 goals in 622 career games for club and country, told Match of the Day he has serious doubts over City's mentality.
"Two things constantly worry me with Man City," Shearer said on MOTD.
"The first being they still haven't addressed the issue of playing without Vincent Kompany despite millions and millions being spent on defenders. I think they're poor at the back.
"And the second is why does it take 70 minutes for them to kick into action or when they're a goal down for them to start playing?
"Why can't they have a bit of urgency from the start of the game from their leaders in the team?"
City could look back at the Vicarage Road result - against a team bang in form and full of confidence - as the turning point in their season.
Many pundits and fans have an obsession stating how much money the Blues have spent on their squad like it is a new phenomenon in football.
The fact is that when City bid for a player the price doubles and given their riches they will always have to do business at over-inflated prices.
What Pellegrini must do, though, is ensure those players are ready for the English top flight when it comes to the crunch because they will be wide open to criticism.
If they can get Kompany back and fit it could be perfect timing to push their title tilt over the line as we approach the business end of this most open of Premier League seasons.