Last year’s Player of the Year nominee took a place on the bench while new signing Olivier Ntcham was given a start for his competitive debut.
This led fans to wonder whether Armstrong had been dropped because of the ongoing wrangle over his contract situation.
Celtic are keen to tie the player down to a long-term deal but negotiations, to this point, have failed to find an agreement.
Yet Rodgers was keen to stress there was no “correlation” between the 25-year-old’s expiring contract and the decision to leave him on the bench for Linfield’s visit.
He said: “There was no correlation. There has been no progress as of yet on the contract. I love working with Stuart.
“If there was any correlation then Scott Brown wouldn’t play, he’s in his last year as well.
“I’ve got to prepare players for the season and I’m fortunate we have a strong squad.
“It was very important for the new players. Oli [Ntcham] has come in and we’re trying to get him game time.
“He had just over an hour and you can see his qualities. Once he gets up to speed, he’ll be a great asset.”
Armstrong came off the bench to net Celtic’s fourth as the hosts ran out 4-0 winners, setting up a third qualifying round tie with Norwegian champions Rosenborg.