Hart has been forced to sit out Manchester City's last three matches having been replaced by his understudy Costel Pantilimon, with Pellegrini giving no indication of how long he is likely to be sidelined.
Seaman, who made 74 appearances for England before giving way to David James in 2002, believes rather than axeing Hart, Pellegrini ought to have given him a vote of confidence when he found himself under pressure.
Seaman told TalkSport: "Hart is brilliant. I was surprised he was dropped by City. He's a quality goalkeeper and is playing big pressure games every week and you can't say that about the other goalkeepers.
"He's by far our best keeper and I was glad Roy (Hodgson) came out and backed him.
"That's what you want as a goalkeeper. It's a shame his own (club) manager hasn't backed him as well."
Despite 15 years of distinguished service for his country Seaman himself was not immune to criticism, notably after being caught off his line by Ronaldinho's free-kick in the 2002 World Cup quarter-final.
But Seaman says such criticism is an occupational hazard for an international level goalkeeper and believes Hart is only going through what his England predecessors also faced before him.
"The stick is always over the top because he's England's number one," added Seaman.
"It happened to me, to David James, to Paul Robinson - it happens when you're England number one.
"But it's our choice to be a goalkeeper and we've seen it happen before so don't be surprised when it does."
- Sports & Recreation