The 22-year-old defender picked up two yellow cards as Ajax went down 2-0 to Luis Enrique's side at the Amsterdam Arena.
De Boer felt Veltman, who has six caps for Netherlands, was unlucky to see red, with his first yellow card coming as the result of a foul that took place when Ajax's Anwar El Ghazi was down injured in the Barcelona box.
However, the coach says the experience could help Veltman in his continued development.
"The first one [yellow card] came with one of our players injured in Barcelona's penalty box. I think in such situations the referee needs to stop the game and attend [to] the player," said De Boer.
"That didn't happen so he [Veltman] fouled a player and so [he received] the first yellow card.
"As for the second, [Lionel] Messi is very fast and he didn't really want to touch him but that's what happens with Messi.
"He obviously needs to improve and be smarter but I reckon it's extremely important he plays this kind of game so he learns and grows as a footballer."
Ajax can no longer qualify for the last 16 of the Champions League, with Barca and PSG guaranteed to progress from Group F.
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