The Red Devils battled to an opening win in Group L against the Kazakhstan Premier League champions on Thursday, with Mason Greenwood's 73rd minute finish ultimately proving to be the difference between the two sides.
With several major names such as Paul Pogba, Anthony Martial and David De Gea either injured or rested, the hosts fielded several youth stars alongside a clutch of senior faces at Old Trafford.
Speaking to BT Sport after the match, Solskjaer admitted that his team found the going tough in parts, with his underpowered line-up finding their visitors tricky opponents.
However, he praised the contributions made by Greenwood, alongside fellow academy graduates Angel Gomes, Axel Tuanzebe and Tahith Chong, among others, who helped seal the win, adding that he intends to play them again over the coming weeks with a Premier League clash against West Ham and Carabao Cup tie with Rochdale to come.
"We made it hard for ourselves," the Norwegian stated. "Games like these you can make sure you win the game in the first 20 minutes if you take one or two of the chances and then you can enjoy it.
"You could see that some of our lads needed games. It's pleasing that we got three points. We got off to a decent start in that respect.
"We think today was a great opportunity for [the younger players]. We wouldn't throw them in if we didn't feel they were ready, but you can still see they need game time.
"You get your rhythm when you play a game every week, so some of them won't play against West Ham but they'll play against Rochdale in midweek."
On Greenwood, Solskjaer expressed his contentment with the teenager's efforts, adding: "We always know that in and around the box he's one of the best finishers we've got and I'm happy he got this goal. I'm sure he'll go home tonight happy with that one.
"If you want to make it as a Man United player, you have to handle the fans. It's not an easy place to make your debut, in a game like this where you don't get a goal but Mason won us the game and we're very pleased for him. I thought Angel [Gomes] did very well, [Tahith] Chong also showed glimpses. They'll be better for it."
Midfielder Nemanja Matic, one of the more senior players to start at Old Trafford, also acknowledged the difficulty of the game but likewise hailed the contributions made by younger squad members, describing them as the 'future of the club'.
"It was a hard game," the Serbia international added. "It's very important to start with three points and we are happy because of that.
"It's good for [young players] to have this opportunity to play these games. They have to use that to work hard to get more chances during the season. I'm happy for them. It's great as it gives young guys a chance to improve. They can only improve if they play games.
"They are young. They want to prove that they deserve to wear the shirt. The time has come for them. They are the future of the club. I wish them all the best."