Solskjaer rung the changes from the 1-0 midweek defeat to Barcelona in the Champions League and United turned in a disjointed performance, as Paul Pogba struck twice from the penalty spot either side of Felipe Anderson's 49th-minute equaliser.
However, Solskjaer was keen to point out that on other occasions during a recent fallow run of form, United had not been so fortunate.
"Sometimes you get more than you deserve and today is one of them. Watford [a 2-1 home win last month] last time was one of them.
"But then again, Arsenal and Watford – the two away games we've lost – we should have won. So it evens itself out in the long run.
"Luckily it wasn't Barcelona on the other side but West Ham played well, played better than us, created chances."
Not for the first time over recent seasons, a United manager was left to marvel at the heroics of David de Gea, who completed an incredible second-half save from Michail Antonio when the score was 1-1.
"We have one of the best goalkeepers in the world," he said. "That save is unbelievable.
"He won us the game because at 2-1 we would have struggled to create enough."
Pogba held his nerve to be United's matchwinner but Solskjaer felt a collective lack of willingness to press with intensity left the France star and his midfield colleague Fred exposed too often.
"We were wide open defensively. We didn't manage to press them and then we were wide open in midfield," he explained.
"I thought Fred and Paul played well but they didn't have the protection and we didn't get to pressing.
"We need to look at that at home – manage to be braver in the pressing, step up from the back and spend more energy winning it higher up.
"We kept giving the ball away so it was end-to-end, like a basketball game at times.
"The intensity was good, if you look at the physical stats, but the control wasn't good enough."
Pogba ditched his previous approach of using an exaggeratedly slow run-up in favour of running up quickly to both penalties and emphatically dispatching them past Lukasz Fabianski.
"It's up to him, he's practicing penalties. He's confident, he's mentally very strong," Solskjaer added.
"I like that way of running up to the ball and smashing it. The second one – the keeper went the right way – was a great penalty."