Mourinho also admitted he was anxious when Phil Jones and Eric Bailly stepped up to take their penalties.
"The penalties come, somebody has to miss".
Sanchez was poor again on Saturday as United were held to a home draw by Wolves and former Gunner Ian Wright hasn't held back in his criticism of the 29-year-old.
"The players were happy with that decision and the reasons behind the manager's decision", the source added.
United started the game in ideal fashion with Juan Mata opening the scoring inside three minutes.
However, an unchanged Derby side struck back after the break thanks to a wonderful free-kick from on-loan Liverpool striker Harry Wilson.
Romero was forced into making a fantastic save to deny Wilson from equalising.
Mourinho confirmed after 8-7 shootout loss for Frank Lampard's Derby that he had made the decision to take the vice-captaincy off Pogba, but tried to claim there was no problem between them.
The France worldwide captained the side in the Premier League openers against Leicester and Brighton in the absence of Antonio Valencia, just as he did in last week's Champions League win at Young Boys.
Tiger Woods caps off amazing comeback with a win
How consistent was Tiger on this day? A year ago, there was no guarantee anyone would see much of Woods, much less Woods winning. The 42-year-old is up to 13th, rising eight places care of his dramatic Tour Championship success at East Lake GC on Sunday.
"It would be a great headline if he scores a hat-trick, so don't ask me", Lampard told reporters.
"I am trying to build a group to be successful and nights like this are incredible". Privately, the club have given their support to the Portuguese coach and while revealing fourth quarter financial results, Woodward said he is also behind the manager.
The visitors dominated throughout but had just the one goal to show for it before half-time as Gabriel Jesus headed home from close range. 'That's Old Trafford. We are here to attack.
And Foden rounded off a fine individual display with his first senior goal for the club in stoppage time.
The Red Devils were looking to return to winning ways following a 1-1 draw with promoted side Wolverhampton Wanderers in the Premier League at the weekend.
Other winners were Middlesbrough, Norwich, Blackpool and Burton Albion.
It prompted a group of supporters to pay for a protest banner to be flown over Turf Moor during the 2-0 win over Burnley on September 2 that read: "Ed Woodward - A specialist in failure".
Fulham's strength in depth was in evidence as they swept aside Championship Millwall 3-1 at The Den despite making 10 changes. We couldn't be dominant in the second half.