Van de Beek, a £40 million summer signing from Ajax, was an unused substitute for the 0-0 draw with Chelsea on Saturday, prompting Patrice Evra to say his former club "don't need him," while former Netherlands forward Marco van Basten said the player should have joined a club where he can play more regularly.
Van de Beek has not started a Premier League game so far this season, managing just 61 minutes in five games, but Solskjaer is backing the 23-year-old to come good.
"I realise the topic is Donny van de Beek and it's nice for some players or commentators to have a little go," Solskjaer told a news conference on Tuesday. "I know you're short for time when you're on telly and you have to put your points across very quickly but you have to know that you don't have to start the first three games to be a very important player in the squad.
"When Donny has played, he's played really well. I think it says a lot about our depth of quality in the squad that we don't have to use him every single game because we have other players as well. I also think it says everything about our ambitions -- we want to push on, we want to challenge for trophies this season. Donny is going to play a big, big part this year. Donny's going to be very very important for us, don't worry about that."
Van de Beek has competition for a place in Solskjaer's midfield, which has not been able to accomodate Paul Pogba for the last three games with the France international consigned to a place on the bench.
Scott McTominay is also challenging for a place in United's midfield and he has told Van de Beek not to "panic" about his lack of opportunities so far.
"I'm so confident Donny will be such an important figure throughout the season," McTominay said. "He's lifted everybody else, along with Alex [Telles] and Edinson [Cavani]. They're top quality players who can lift the dressing room.
"It's no time to panic for Donny. You can be so quick to come to an assumption that he's not playing but you need to give him time and let him adapt."
It will also give Solskjaer the chance to run the rule over defender Dayot Upamecano, who was linked with a move to United in the summer.
"There's always rumours and speculation about good players for Manchester United, but since he's playing against us, I know he's a very good player so we can see him close up," he said.