Said Benrahma's deflected effort sent the Hammers ahead in the 30th minute of the contest, but Cristiano Ronaldo's close-range finish levelled the scores 10 minutes before the end of the first period.
Solskjaer was not pleased with his team's defending for the opening goal of the match but has hailed the "great response" to conceding first at the London Stadium.
"We've spoken you can't take risks when you defend and we dropped into a back six and it's too many spaces, too late to charge the ball, we've already sorted and spoke about that at half-time so it was better second half," Solskjaer told Sky Sports News.
"Great response, for me it was how to do you respond to going 1-0 down and a very, very good five minutes for us."
Man United will again face West Ham on Wednesday night, with the two teams locking horns at Old Trafford in the third round of the EFL Cup. body check tags ::