Hallgrimsson, who added he is a “sore loser”, said he felt better about the organisation of his side in the first half against Greece, compared to the first 90 minutes of his reign against England.
He added that the Republic were “punished” for not taking their chances before Ioannidis’ superb opener early in the first half.
“That happens to teams who are lacking confidence. It’s the details in decision making, etc,” said the 57-year-old.
“Greece are a team who are difficult to play against when they are one goal ahead.
“It was tough when we conceded the first goal because I thought we played pretty well until then. The first half was good in the eyes of organisation and compactness.
“We didn’t give them chances and had really good options when we were going forward.”
With fixtures away to Finland and Greece to come in October, Hallgrimsson said he needed to find a swift solution to the issues facing the Irish.
“The solution is to find these connections and the understanding between the players,” he said.
“My job is to turn this around – nobody told me it was going to be an easy job.
“I know it is going to take time but I feel that the first step is positive. Even though we lost the two games I feel that the first step is positive.”