"You're always measured on results but we played a good game against Arsenal, [we've] played so much worse and won games and that's the odd thing when you're a manager you can look behind the result and say that was a good performance didn't get what we deserved", Solskjaer said in his pre-match press conference.
"We can go all the way, but you've got to be lucky and good".
Bale has been at Real Madrid since 2013 and is a four-time victor of the Champions League, although there is no chance of a fifth this term after bowing out to Ajax in the round of 16.
This year is the 20th anniversary of United's treble-winning season, when they won the Premier League and FA Cup as well as the Champions League, with hard moments on the way to all three trophies. "And the mood is good, the training attitude is good, so hopefully we can keep that run going".
Despite the defeat, Solskjaer - whose side travel to Wolves for an FA Cup quarter-final on Saturday - has no issues with United's performance and believes they were unlucky to lose.More news: Mosque Massacre: A hate-fuelled attack on values that unite us all
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"I believe that you get what you deserve in life, in sport", he said.
"Every single game that you win puts another layer on that, on the way to becoming the team that we want to be".
"We regularly review our intelligence to make sure our officers are where they need to be, but you can help too".
"I think I've answered that question quite well here", he said with a smile.
"We've shown against PSG that on any given day we can beat a top team, but then again there are so many variables and in these games things are decided by margins".