Eddy, a first-team Class AAA All-State player last season, led all scorers with 15 points, but never got into rhythm.
One of his few uncontested shots was a jumper just inside the 3-point circle that tied the game at 27 with 4:24 left.
"I took one dribble and there was a guy flying at me this way at my left, and a guy coming the other way," said Eddy, whose only rest before picking up his fourth foul at the 19-second mark of the fourth quarter was a 3.4-second break at the end of the third. "They had a good game plan. It worked ... first game."
He also finished with eight rebounds, three assists and three steals, but seldom got loose. Only four Patriots scored with senior Austin Breeden and King scoring seven apiece and freshman Cam Hoston adding six to go with seven rebounds off the bench.
Capital had eight scorers, led by junior Carrington Morris with eight, Tyrhee Pratt with seven and Austin Coleman with six.
"Luke and Austin were the only ones who have played any varsity minutes," GW Coach Rick Greene said. "It's going to take time. If you look at the whole thing until March, it's pretty encouraging that we come over here, lead with a chance to win it actually, considering where we are right now.
"I hate to lose and I'm disappointed we lost, but I'm not discouraged by anything at all. Some of the things we didn't do have to do with experience and some better practice habits."
The low-scoring affair featured 68 missed shots and only two 3-point baskets - one by GW's King with 3:24 left in the first quarter, and one by Capital's Pratt to give the hosts a 14-6 lead with 5:38 left in the first half.
The Patriots missed eight of their 3-point tries, while the free-shooting Cougars were 1-of-19 from long range.
George Washington faces Spring Valley on Friday in its home opener. Capital will play its third consecutive home game on Friday when it entertains Hurricane, which is coming off a 67-60 upset of host Logan on Monday night.