The Tigers targetman was twice picked out in dangerous areas by inviting left-wing crosses from the boot of Mallik Wilks, but although he found himself unmarked on each occasion, he failed to ripple the back of the net.
The 28-year-old has played second fiddle to Josh Magennis for much of the season, though his team-mate's recent Covid-19 issues have opened the door for Eaves to start City's last two fixtures.
The Liverpudlian's record of three goals in 15 League One appearances so far this term isn't as bad as it sounds given that he has only started four of those games, but what is concerning, is the number of good openings that Hull's number nine is squandering.
A simple headed opportunity directed straight at the goalkeeper and a wild, rushed effort blasted over the cross-bar when through on goal against Charlton last time out were quickly forgotten because the Tigers went on to win that contest comfortably in the end.
But, on Saturday evening, City dropped two points and missed out on the chance to move within in touching distance of league leaders Lincoln as a result of the profligacy of Eaves in particular, but also Wilks.
Eaves' first chance of the night looked the easiest of the two, but he could only plant a free header against the frame of the goal, while his second effort was saved by Sunderland custodian Lee Burge as Aiden McGeady struck to cancel out Reece Burke's 13th-minute opener on Wearside.
McCann, however, was able to take some positives from his centre-forward's performance.
Asked whether Eaves has to start taking his chances sooner or later, the Tigers head coach replied: "Yes, any centre-forward will tell you that.
"The fact that he's getting the chances pleases me, if there's no chances coming his way then that's a worry.
"He's had two good chances tonight. One he's hit the cross-bar, which was a little bit unlucky. The second one he may have had a bit more time but he's tried to direct it back across [goal] and he's done the right thing.
"We're disappointed that we didn't win the game because we felt as if we had the better chances, but we'll take the point."
Eaves was denied the opportunity to atone for those misses later on in the game, pulling a calf shortly before half-time and limping off the field to be replaced by Magennis.
"We might need a number nine now, it depends on how Tom Eaves' calf is," McCann added.
"We'll see how he is in 24 or 48 hours."