United failed to have a single shot on target in an uninspired showing and have now failed to win in their past 10 away games.
But Solskjaer saw the game positively and focused on a penalty he felt his side should have had when Stijn Wuytens brought down Marcus Rashford with 10 minutes to go. The referee did not award it and the video assistant referee system is not in use in the Europa League group stage.
“I’m very happy with the boys,” said Solskjaer. “It should have been three points.”
He said “you can’t even discuss” the penalty decision because it was so blatant and added they should have had a spot-kick during Monday’s 1-1 draw against Arsenal for a Sead Kolasinac handball.
“I couldn’t believe what I saw, same as Arsenal with the handball,” he said.
“It’s frustrating getting these little things. The boys deserve so much more. It’s going to turn at one point and we’ll get the decisions and then they’ll get the results we deserve.”
Solskjaer had earlier criticised the plastic pitch as one of the “worst ones I have seen for a long while”.
“This is a good performance and a good point against a good opponent on a bad surface,” he said after the game.
But it would be hard to blame the surface for United’s failure to test the goalkeeper once, with Jesse Lingard hitting their best chance wide late on.
AZ had the better chances, with striker Myron Boadu having a first-half goal correctly ruled out for offside.
Substitute Lingard walked off with a hamstring injury late on, leaving United to end with 10 men – and Solskjaer expects him to miss Sunday’s Premier League game against Newcastle.
United have not won in their past four games in all competitions, excluding a penalty shootout victory against Rochdale.
They are level with Partizan Belgrade on four points at the top of the group. The Serbian side won 2-1 in Astana thanks to a double from Umar Sadiq earlier on Thursday.
United’s struggles continue
United have not won an away game since beating Paris St-Germain in their famous Champions League win in March.
They made eight changes from the lacklustre 1-1 draw against Arsenal on Monday – but this was no under-21 squad. In fact their starting line-up had an older average age than AZ’s. Six of the 11 were over the age of 25, including goalkeeper David de Gea and midfielders Fred, Nemanja Matic and Juan Mata.
Mason Greenwood got the chance to start up front that some people expected on Monday, but he had one shot which looked goalbound before being blocked by Ron Vlaar.
It took United 67 minutes to have a shot, excluding blocked ones, with Angel Gomes hitting well over from distance.
United brought on Rashford, Lingard and Scott McTominay as they looked for a winner, but it never really looked on the cards.
The positives were a decent defensive performance – with Brandon Williams making a first start at left-back – a clean sheet and a point.
A few strange bounces on the artificial turf caught players off guard, with plenty of passes cut out – but then that was also the case for United on their own grass pitch on Monday.
AZ are third in the Dutch league and now unbeaten in six games – and they had the better chances.
Netherlands Under-19 teenager Boadu had the ball in the back of the net with a stooping header from Fredrik Midtsjo’s cross but he was well offside.
The 18-year-old had another chance but he did not make proper contact with a header.
Alkmaar winger Oussama Idrissi was excellent, causing Diogo Dalot plenty of problems, and he forced two saves from De Gea as well as shooting wide from long range.