The two sides drew 0-0 in the Scottish Premiership clash - which followed a 1-1 draw at Celtic Park earlier in the season - as the visitors ended a poor run of league form.
Tommy Wright's side had won only one of their previous eight games since beating Rangers at Ibrox in December - against Albion Rovers in the Scottish Cup - before Sunday's encounter in Glasgow.
"I think there are questions there for Tommy's players," Rodgers told BT Sport after the stalemate. "Tommy's a fantastic manager but I am sure he walks away happy with a point but probably really frustrated.
"How can you win a game 3-1 at Ibrox in December 16, not win a game right the way through, apart from the Albion game then your next big result is away at Celtic?
"So I think the question goes with the St Johnstone players. Today you've seen them organised, committed, fighting, running - doing all of that. If they do that in every game they would probably win a lot more games."
Rodgers had made seven changes to the Celtic side which started in the 1-0 win over Zenit St Petersburg in the Europa League on Thursday night.