It finished a tough week for the defending champs.
Barry admitted: "This was massive. Playing three games in seven days is always tough.
"It wasn't the greatest performance but the manager said at half-time to stay calm and we would get a goal and we found a way.
"Carlos came up with the goods and it was a fantastic goal.
"You have to give Swansea credit, their gameplan was good, they sat quite deep and made it tough for us to get the ball forward. The second half we pressed them higher and eventually got on top.
"They played a good game but it was a massive three points for us."