Steel, 19, kept his place in goal after making his debut in the Carling Cup win at Chesterfield in midweek.
Strachan said: "Today was Jason's day. I don't think the Leicester camp and supporters realised just how young Jason is. He looked like a man with his performance today.
"He shows respect on the training ground and in everything he does. He has great confidence."
Leicester's Wales international Andy King almost unlocked Boro's defence in the eighth minute when he headed against the bar from Matt Oakley's corner.
Steele then clawed away Campbell's 25-yard free-kick before getting his body firmly behind a drive from the same City player.
In the second half Steele rescued Boro again with a superb fingertip save to keep out a 20-yard drive from Steve Howard.
Both sides are eying a promotion bid this term but suffered shock opening day defeats to Crystal Palace and Ipswich.
Leicester: Weale, Neilson (Lamey 82), Berner, Hobbs, Moreno, Wellens, King (Gallagher 74), Oakley, Howard, Campbell (Fryatt 82), Dyer. Unused substitutes: Logan, Morrison, N'Guessan, Kennedy.
Middlesbrough: Steele, Hoyte, Bates, Wheater, McManus, Bailey, Thomson (Lita 71), Luke Williams (O'Neil 46), Robson, Boyd (Kink 85), McDonald. Unused substitutes: Coyne, Miller, Arca, Hines.
Referee: M Jones (Wales).
Man of the match: Jason Steele.