Kai Havertz's 16th-minute goal settled Sunday's contest at Anfield, giving Arsenal their first league victory at the ground in 14 years and moving them three points clear at the top of the Premier League.
Liverpool had opportunities to recover from the early setback. Florian Wirtz struck the crossbar with a free-kick, while Alexis Mac Allister headed over as the hosts searched for an equaliser.
The most contentious moment came when Isak was pulled back by Timber inside the penalty area as he attempted to reach a cross. The Liverpool forward stayed on his feet, but the appeals were rejected by referee Andy Madley and upheld following a VAR review.
Van Dijk was unconvinced by the decision when asked about the incident after the final whistle.
"I think it was a clear penalty. I've seen it back and I've seen it being given. Today it wasn't meant to be," he said.
The Liverpool captain was also asked whether Isak should have made more of the contact to attract the referee's attention.
"We have 50 cameras. Why does he have to complain when there are so many cameras?
"Everyone has seen it. In the end it wasn't given and we lose the game unfortunately, so well done to Arsenal."
Van Dijk was disappointed with Liverpool's overall failure to turn their pressure into a goal, although he felt the team's response after falling behind had been encouraging.
"Disappointed," he added. "We play at home, we had some opportunities. We tried everything. We could have done a bit better in the last 15 minutes to get more balls in the box.
"It wasn't enough today and that's why disappointment is the feeling I'm having. When we conceded we played much better. Alexis could have changed the game."
Liverpool manager Andoni Iraola also believed the decision on Isak was incorrect, arguing that the shirt pull had prevented the striker from making contact with the ball in a dangerous position.
"The Isak one is a clear penalty, they grab him, everyone see the shirt and probably because he doesn't dive," Iraola said.