Mr Baty, speaking on United's third-quarter earnings conference call, outlined the impact of failing to win the Europa League, thus missing out on Champions League qualification.
"We made seven changes and with a good result and good play and we saw all the squad play with good concentration and focus and this is the most important thing".
Carrick claimed he did not want to sign fresh terms "for the sake of it" but has played a key part in Mourinho's first season.
They are also out to avenge their 3-2 defeat by United in February's League Cup final, which left a bitter taste after Manolo Gabbiadini saw what would have been the opening goal ruled out for a dubious offside.
The club's forthcoming summer tour features one game in Norway, and five games in the US.
The clash in Stockholm will be United's 64th match of an epic season - and Mourinho admits it has been hard to get through the year amid a succession of injuries to the likes of Zlatan Ibrahimovic, Eric Bailly, Luke Shaw and Marcos Rojo.
While De Gea's time at United appears to be nearing an end, Michael Keane looks set to return to the club after leaving Old Trafford for just £2m during Louis van Gaal's reign.
Jose Mourinho has discussed how he will juggle his resources in Manchester United's final two games of the Premier League season, in order to be able to field the strongest and freshest available team for next week's Europa League final.
"The accumulation of the games, I never had that", Mourinho told a news conference on Tuesday. And I went out at the last 16 stage once.
- Jose Mourinho is likely to name a weakened side with his priority on their Europa League final against Ajax later this month. The three-time Premier League winning manager expressed his frustrations at the pair's cautious approach to recovering from injury, during a season which has seen United plagued with a defensive injury crisis.
"I am giving one-day holiday "a la carte", if you understand - Blind one day off, [Henrikh] Mkhitaryan one day off, [Ander] Herrera one day off", he said. As far as United are concerned, they might try to push for a draw since they can not afford to lose again.
Addressing United's underwhelming season, Smalling conceded: "It does eat away at you". Because if we go to the FA Cup semi-finals it would be a total disaster.