For the second week in a row the Swifts pushed the big guns all the way, but ultimately left empty handed.
Last week they went down 1-0 at Windsor Park against Linfield, and seven days later they were beaten by a similar score away at league leaders Coleraine.
“I’ve been frustrated the last two weeks as we have created a lot of opportunities against Linfield and Coleraine," he said.
“Coleraine had a lot of shots on goal, but Stuart Addis hasn’t been overly tested or worked.
“We had a couple of good opportunities in the second-half that probably landed at an area which was comfortable for Chris Johns.
“We are frustrated because we have put in two decent performances, it was hard to play on a heavy pitch today, but whilst we can take positives, we have come away with no points.
“If we keep putting those types of performances in, then we will be alright.
“We had a couple of good breaks from midfield in the first-half.
“Grant Hutchinson and Douglas Wilson both broke free, but if those chances fall to different personnel we have a better chance of scoring as they don’t get many goals.
“From Dungannon Swifts point of view, we have to take positives from it. We got to appreciate the effort the boys have put in over the last two games.
“I feel for them because they deserve something for their efforts, but all we will ultimately get is a pat on the back."
McAree revealed he changed tact for Saturday's game in a bid to rattle their opponents.
“We knew the pitch was going to be heavy, so we came with a plan to make sure we stayed in the game for as long as we can," he said.
“We introduced Cormac Burke, Ryan Mayse and Peter McMahon which gave us that attacking presence.
“Even if the game was a draw, we were still under the impression that we would have made those changes.
“They did extremely well when they came on and got closer to Johnny Lafferty."