“There is a now a little bit of hope where there wasn’t a few weeks ago,” Shearer told BBC Radio 5 live.
“They should have got him in earlier. If they’d done that I don’t think we’d be in this position.”
Newcastle’s point came after Vurnon Anita’s first goal in more than two years cancelled out a controversial opener from Sergio Aguero, who headed in from an offside position.
The hosts almost won the game when Georginio Wijnaldum was denied by Joe Hart’s late save.
Victory over Swansea on Saturday marked a first win for Benitez since succeeding Steve McClaren, and his team are now two points behind fourth-bottom Norwich, and one point behind rivals Sunderland, who have a game in hand.
‘Benitez leaves players out for a reason’
Shearer, who scored a record 206 goals for Newcastle over 10 seasons, said that despite his late appointment, Benitez had changed the mood around St James’ Park.
“Certainly on Tuesday’s evidence, and on Saturday’s, there’s now a togetherness,” Shearer added. “The fans appreciate now that the players are giving everything. They’ve given themselves an opportunity – three points on Saturday and a point tonight which is not a disaster.
“It’s taken him a while to understand his players but he’s left big players out. Aleksandar Mitrovic is out, Jonjo Shelvey is out, they’re out for a reason, they’ve not given enough to the team.
“He’s changed it and he deserves credit for that. The atmosphere stood out. The crowd gave the players an applause at the end and when that happens fans can’t ask any more.”
‘We can beat anyone’
Benitez, who takes his side to former team Liverpool on Saturday before their Europa League semi-final at Villarreal the following Thursday, said: “We have to try to win every game, it doesn’t matter where.
“My connection with Liverpool is obvious, it’s quite good, but hopefully they will do really well in the Europa League and we can get three points in the Premier League.
“At the moment, it’s true that we are doing well, so hopefully the game away against a very good team like Liverpool, we can see the same things. But you never know.
“What we have is belief,” the Spaniard added. “We believe now that we can fight, we can beat anyone and in the next games, we have to show that.”