The pair have impressed since joining the Hoops in January, with onlookers calling for Scotland boss Strachan to offer them international call-ups.
The 58-year-old, however, says the Celtic duo have far more to prove than what they have in only a few games for the Scottish champions.
Indeed, Strachan says the Bhoys' form doesn't quite make them superstars, warning that they were struggling to get into the starting XI of their former side earlier this season.
He said: “Armstrong and Mackay-Steven have played three or four games for Celtic and you have to remember that in September both of them were left out of the Dundee United first team.
“So just because they’ve pitched up at Celtic doesn’t make them superstars but, by the same token, those two lads have been in the squad before. It’s hard to pick young lads when they aren’t playing for their first teams."
Strachan did, though, hint at a future call-up, suggesting he is delighted with the 'education' the young duo are receiving with the Bhoys.
Mackay-Steven and Armstrong both played big parts in Celtic's Europa League ties with Inter Milan, while they have also made a big impact domestically.
And the Scotland boss has acknowledged that it's great to see the pair plying their trade in front of a packed Celtic Park.
He added: “But it’s great to see over the last few weeks that they’re playing in front of 60,000 people. That’s great for their education."
Celtic face Dundee United in the Scottish Cup quarter-finals later today, before facing the very same team in the Scottish League Cup final next Sunday afternoon.