"It's in our hands," said McLeish. "I'm challenging the players to win all our games.
"We've got to believe we can and have a strong mentality.
"Sheffield United have hard games left, the same as us. Nobody has an easy game but it comes down to temperament and how much the players want it because there is nothing between the teams."
McLeish was grateful to a poor miss from Zheng Zhi, who managed to hit last defender Stephen Carr with the goal gaping, an offside flag which denied Darren Ward and a stunning late save from Maik Taylor to preserve a point.
Taylor somehow stuck out a hand to claw away a deflected effort from Charlton teenager Jonjo Shelvey as the rock-bottom hosts pushed City all the way.
"They are fighting for their status in the league so we never expected anything different," added McLeish. "We never thought we would just be able to turn up and win.
"Maik made a brilliant save. He has had a fantastic season, he's been first class.
"We had to earn the the right to win here and we didn't earn it. A draw was probably fair."
Charlton now look a world away from the team which lost its way so spectacularly under Alan Pardew earlier this season.
But their improvement has come far too late to save them, and they are now 12 points from safety with just five games remaining.
"If we had had that team out there on the pitch earlier in the season we would be nowhere near the bottom," said Addicks manager Phil Parkinson.
"This team is a good team. We've got some good players and we've gone toe-to-toe with a team looking for promotion and at times made them look very ordinary.
"It was an excellent save from Taylor, and we feel Darren Ward's disallowed goal was onside. So it's disappointing because we should be talking about a very good victory."
The Addicks head to Coventry on Easter Monday knowing defeat will probably send them down.
"That's the harsh reality," added Parkinson. "We needed to win the game, but I don't think we could have done much more to win it."