Despite winning in four sets, Berdych was angry with Almagro for hitting him with a shot as he approached the net.
Almagro apologised to the Czech but the seventh seed was clearly angered by the incident.
"What happened from Nico was not what should be happening in tennis," said Berdych. "Maybe we both made a mistake, so it's even and that's it."
The 26-year-old was booed by the Hisense Arena crowd after refusing to reconcile with Almagro at the end of the match.
Berdych will face Rafael Nadal in the quarter-finals.