In a game of few chances at the Cars Jeans Stadion, United substitute Rashford went to ground under a clumsy challenge from Stijn Wuytens during the closing stages.
After the match, Solskjaer bemoaned a familiar theme of a sapping week – recalling how claims for handball in the box against Arsenal defender Sead Kolasinac similarly fell on deaf ears during Monday's 1-1 draw at Old Trafford.
"It's a penalty 101 times out of a 100," Solskjaer told BT Sport.
"How many times this season have we not got penalties? Against Arsenal that would be 2-0, tonight would have been 1-0.
"It would have topped off a very good performance away from home against a very good team. We've come here and should have won."
United goalkeeper David de Gea repelled their Eredivisie opponents with a couple of sharp saves and reported Rashford was convinced he should have been awarded a spot kick.
"From my position it's really difficult to see that," he said. "We asked Marcus and he said 100 per cent it's a penalty. I didn’t see well from my position but it's probably a penalty."
As it was, United did not manage a shot on target during the contest, but they have four points from two outings in the Europa League and Solskjaer was keen to focus on the positives.
One of those was an assured full debut from 19-year-old left-back Brandon Williams.
"Top class. You don’t see a better full debut from a full-back anywhere," Solskjaer added. "The boy is just going to improve and improve."
The draw leaves United without an away win in their last 10 games across all competitions, their worst run for 30 years. In that period, they have lost six times, failing to record a victory away from Old Trafford since their 3-1 win against Paris Saint-Germain in the Champions League in March.