Some British newspapers reported on Tuesday that Shaw and Smalling are fighting for their futures at Old Trafford.
While not mentioning either player by name, Mourinho expressed unhappiness after the pair missed United's 3-1 win at Swansea City on Sunday, suggesting they had shown a lack of bravery.
Some British newspapers reported on Tuesday that Shaw and Smalling were now "fighting for their futures" at Old Trafford.
Left-back Shaw, 21, was said to be "baffled" over his treatment by Mourinho, who succeeded Louis van Gaal as United manager in May.
The England international recently spent 11 months on the sidelines after sustaining a horrific double leg fracture in a Champions League game at PSV Eindhoven in September last year.
He has been in and out of the team since making his first-team comeback in August and is reported to have felt pain in the leg he broke during last Thursday's Europa League defeat at Fenerbahce.
Mourinho said Shaw had informed him he was unable to play against Swansea on the morning of the game.
But the former Southampton player is not thought to have travelled down to south Wales with the rest of the squad on the eve of the match.
Mourinho also singled Shaw out for criticism following United's 3-1 defeat at Watford in September, after which it emerged the full-back had been playing with a groin problem.
"Our left-back is 25 metres' distance from him, instead of five," Mourinho said after Shaw failed to close down Nordin Amrabat in the build-up to Watford's second goal.
Smalling, 26, has tended to start for Mourinho when fit, but the Portuguese appears to have lost patience with the England centre-back, who has missed four games with a foot injury.
Both Shaw and Smalling are thought to have played with pain-killing injections already this season and interim England manager Gareth Southgate has defended them against accusations they lack heart.
Asked if the pair are "a bit flaky", Southgate told reporters at England's St George's Park training base: "I don't know Chris well. That wouldn't be my impression, having worked with him.
"Luke I know well and Luke's had a really tough injury. Very often it's easy to look from the outside or make judgements on people without knowing them really, really well."
Shaw and Smalling were both left out of Southgate's squad for England's World Cup qualifier against Scotland on Friday and next week's friendly with Spain.
The Sun reported United's senior players have accepted Mourinho's hardline stance over Shaw and Smalling.
Mourinho was hired to restore some of United's fading lustre after three seasons of underachievement under David Moyes and Van Gaal.
He notoriously thrives on conflict and is renowned for publicly rebuking players to test their mental fortitude.
It was an approach that worked wonders in his first spell at Chelsea, where players like John Terry, Frank Lampard and Didier Drogba became unflinching allies.
Terry, who remains at Chelsea, is known for putting his body on the line and said in 2010 that he been taking anti-inflammatory injections prior to games for five years.
Recalling an injury he sustained during a match against United in April 2006 that left his ankle "pouring with blood", he told the Daily Mail Mourinho "wouldn't even look at me".
But there is a feeling Mourinho's methods are not as effective on the younger, more mollycoddled generation of players he has encountered in his second spell at Chelsea and now at United.
Belgium internationals Kevin De Bruyne and Romelu Lukaku both failed to win Mourinho's trust at Chelsea, but are now thriving elsewhere -- De Bruyne at Manchester City, Lukaku at Everton.
With United a lowly sixth in the Premier League table, eight points adrift of leaders and arch rivals Liverpool, the club's fans must hope Mourinho's formula has not passed its sell-by date.