Barnsley came close but weren't rewarded for the second half pressure they put the hosts under.
"I thought, first half, they were brighter than us," said Johnson. "Our back four showed a bit of fear in their play and conceded another poor goal after we got back into it.
"We rallied and, second half, we were the better side. The lads were playing for everyone, Coventry are a good side and we penned them in. We should have had another penalty and quite a few attempts at goal.
"Pearson, Scowen, Isgrove and Mawson were fantastic, they were excellent.
"We keep conceding goals from basic errors, it’s far too basic. It’s not the way the errors are coming it’s the timing of them. At 2-1 we are in the ascendency then we give another poor goal away.
"We’ve come away to a good side it was always going to be difficult and we’ve been clapped off. It won’t be long before we pick up results, I’m sure of it. A couple of players will be coming back and even that side today looked good enough to gets results."
"The one thing that I felt was weak, was that it is very easy to play at 3-1 down. What you must do is have the same attitude at the start of the game as we did the second half. We had some fear in our team which played into their hands, and their chances were from us giving it away.
"I bet if we saw the shot count there won’t be much in it. Their good chances were from poor errors."
The Barnsley boss now has back-to-back cup ties with a trip to Altrincham on Saturday before hosting York in the Johnstone's Paint Trophy next Tuesday.
"We’re short at the moment, we’ve got injure," he added. "Our bench tonight was really young, maybe a bit too young. It’s really important that we get a win Saturday and then Tuesday.
"If we play like that we will. We will fully respect the opposition but it’s a big game for us now, the players can’t treat it like a first round tie it needs to be a cup final. We’ll take an abundance of fans I’m sure and I hope everyone enjoys their day."
