Diaz, who has been one of Bayern's most influential players this season, scored and provided an assist in the comfortable win at the RheinEnergieStadion.
However, the 28-year-old was again guilty of spurning a clear chance when he fired over the bar in a one-on-one with goalkeeper Ron-Robert Zieler, similar to his miss against Borussia Monchengladbach in last weekend's Bundesliga match.
Eberl, though, has said there is no reason for concern and instead praised Diaz's all-round contribution to the team.
"We're extremely happy with Luis," Eberl told reporters after the match. "His intensity and his willingness to be involved both offensively and defensively are outstanding."
The Bayern board member also pointed to Diaz's work rate and consistency in getting into dangerous positions. "You could say he had a big chance at Gladbach, and he had a big chance today," Eberl said.
"But he keeps getting into those positions! He makes those 60- or 70-metre sprints, and not just forward, but back as well. That's why he's an absolute asset for us."
Diaz's goal against Koln took his tally to six goals and three assists in all competitions this season. Bayern, who have now reached the round of 16 in the DFB-Pokal, return to Bundesliga action on Saturday when they face Bayer Leverkusen at Allianz Arena.
Borussia Dortmund head coach Niko Kovac has hinted at several changes to his line-up ahead of Friday night's Bundesliga match at FC Augsburg, following a gruelling 120-minute cup tie against Eintracht Frankfurt in midweek.
Jonas Urbig has praised Bayern Munich's mentality and team spirit after playing a starring role in their 4-1 comeback victory over FC Koln in the DFB-Pokal second round on Wednesday.
Bayern Munich's blistering form under Vincent Kompany reached historic levels as they stormed into the DFB-Pokal round of 16 with a 4-1 victory over Koln.
Borussia Dortmund star Julian Brandt explained giving the captaincy to Nico Schlotterbeck in the loss against Eintracht Frankfurt in the DFB Pokal on Tuesday.
