In-form attacking duo Neymar and Lionel Messi eased the hosts into a 2-0 first-half lead at Camp Nou on Tuesday.
Neymar, Messi and the excellent Andres Iniesta left the action early as home coach Luis Enrique cast an eye towards Saturday's pivotal La Liga showdown with Real Madrid and Ajax rallied impressively in the closing stages.
Ajax substitute Anwar El Ghazi reduced the arrears in the 88th minute before Sandro sealed the points in stoppage time as the Dutch champions pushed for an equaliser.
De Boer took pride in the way his young players responded to adversity but bemoaned the damage done during the game's opening stages
"In the first half it was not really a match," he told UEFA.com.
"One can show a bit of respect for an opponent, but there are limits to that.
"After the break I saw a different Ajax. During the break I told my players they should have more faith and I saw that after.
"When you play against Barcelona you know you will lose 18 out of 20 times. That is how it is.
"They have fantastic players; we have fantastic up-and-coming players."
Ajax full-back Ricardo van Rhijn almost got himself on the scoresheet in an impressive second-half performance but he joined his manager in criticising the lack of resistance to Barca's earlier assault.
"Only at 2-0 was there a bit more space for us and we got back into the match a little bit," he said.
"It is true that there was a very big difference in strength. It was a disappointing evening for us."
"We did not stand a chance in the first 25 minutes. In the first half we did not dare to play football and when we did have the ball we were not secure enough."
