Ipswich took the lead just before the break when Daryl Murphy headed home following poor Barnsley marking from a corner.
The away side responded in the second half, though, and Jim O'Brien tucked Paddy McCourt's cross away nicely.
Speaking to Sky Sports after the game, Flitcroft thought his side did enough after equalising to win the game.
Flitcroft said: "I though we deserved more from that second half showing. We have watched Ipswich four or five times and I think they are in a false position as they are one of the top teams in the division.
"In the first half we didn't match their commitment and desire but in the second half we did and they couldn't live with us. The tempo of our play was fantastic and I am happy with quite a lot of the performances.
"But, in the end, Jim O'Brien's performance and energy was the difference for us. Jim has been out of the team but has always been in and around what we have been doing. He's a great supporter from the bench but his quality, effort and enthusiasm lifted the whole team."
Flitcroft had spent most of the week working on Barnsley's shape and couldn't hide his disappointment at conceding the opening goal from a corner.
Flitcroft added: "It's hard to take for a manager. We have done set piece previews and we've not dealt with it. I can't express how upset we are with that but it's back to the training ground to continue and improve.
"I've a good set of players and they'll believe after this result now. We now need to pick up the volume of points."
Ipswich manager Mick McCarthy thought his side could have lost the match in the end and didn't know why Aaron Cresswell decided to speak to the referee after the game, which resulted in his player being shown a red card.
Also speaking to Sky Sports after the game, McCarthy said: "We were second best in the second half and we could have lost that game, so yeah it's frustration.
"I don't know why he (Aaron Cresswell) went and spoke to the ref. Maybe more frustration.
"When we look at the game in the cold light of day it's what we did do in the first half and what we didn't in the second. They won more headers and second balls and they played on the front foot and played some good football and got the impetus away from us."
McCarthy continues to be linked with the Republic of Ireland managerial vacancy but wouldn't be drawn on his own future.
McCarthy added: "I've said all along, I haven't been asked about it and I don't see why I should have to answer about it, but questions are being answered.
"In the end, though, I think you'll find Martin O'Neill will get the job."