United were second best for the majority of the first-half but led 2-1 at the break, with Robin Van Persie extending the lead in the second period to keep Van Gaal???s side third in the Premier League.
“I think the manager was shocked at half-time,” Smalling said.
“The manager said in the dressing room that the first half was unacceptable and all the players know that.
“It wasn’t a 3-1 scoreline game. Especially in that first half, we all let ourselves down. We could have played much better.
“That first half was probably the worst we’ve had all season, we were lucky to go into the break with a lead.
“We knew that it wasn’t good enough in the first half. We were lucky to get away with it, and we had to stand up and fight in the second-half.”
Van Gaal is set to meet with the club???s co-chairman Joel and Avram Glazer over the next 24 hours to discuss plans for the summer.
Meanwhile, the Dutchman will be preparing for next Monday’s FA Cup fifth round clash at Preston, a competition that presents Van Gaal with a chance of ending his first season at Old Trafford with a trophy.
“We need to make sure that we come out of the blocks quickly against Preston,” said Smalling.
“But If we can win games playing that badly, then it shows that if we do play well and it all clicks, then there will be a lot better performances at Old Trafford, that’s for sure.”
Although it wasn???t the perfect display from United against Burnley, Smalling can be pleased with his personal performance after heading in two goals.
The former Fulham defender, who replaced the injured Phil Jones before notching his first ever brace, said: “It’s not something I’m used to. But because of our first-half performance I couldn’t get too overjoyed at half-time.??
“From one to 11, I don’t think we were good enough, but it’s always nice to score.
“It was great to get the (second) goal before half-time because I think that settled us, and we were more composed after the break. It was a lot better, and a bit more like Manchester United.”
Along with Jones, midfielder Daley Blind also went off in the first-half after suffering a minor head injury, however it???s likely he will recover and feature this weekend.
“In the last couple of games we’ve been able to have a fully-fit squad, so it’s unfortunate that we’ve picked up a couple of injuries,” Smalling added.
“It seems that whenever someone comes back, another drops out. It’s been unfortunate, but hopefully they (Blind and Jones) won’t be out for long.”