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Gillingham boss Steve Lovell had to admit the better side won on Saturday.
The Gills had a sniff at 2-1, after Josh Rees pulled a goal back early in the second half, but a third goal killed them off.
Swansea added another before full-time to seal the fourth round FA Cup win.
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Report & pictures: Swansea 4 Gillingham 1
Reacting to the loss, Lovell said: “They worked very hard, they gave everything, they couldn't have given any more and there was a spell in the second half when we got back to 2-1 and I thought we might have a chance of nicking one.
“The third goal kills you doesn't it? It was a great goal, top quality, but Swansea are an excellent side, a good passing side.
“First half they gave us a lesson of how to pass the ball around, create things and score goals. Second half we changed it up and we put someone on Oli McBurnie (who scored Swansea’s first half goals).
“He was excellent first half but we put someone on him and he didn't get in the game so much second half, it allowed us to pass the ball through midfield and create opportunities.”
Rees headed home to half the deficit early in the second half and it was game on.
Lovell said: “The crowd had gone a bit quiet because Swansea weren’t having as much of the ball as they were, there were patterns of play going for us, we were getting into wide areas. We had good opportunities to do better with the ball than we did, but we were up against a top quality side and they get in your face and stop you doing that.
“I was pleased in the second half, we could get it down and pass it, and use our strength which was out wide and we created a few chances.”
A golden chance came on the break but with Eaves in possession and substitute Brandon Hanlan well placed, the chance went begging.
“That is the frustrating thing with football,” said the manager.
“These things you can’t legislate for, you are 2-1 down and on the front foot, you are going forward and you think ‘hang on this is a chance’, but it comes off Tom’s toe. Swansea pick it up and it’s in the back of our net from a 25-yard thunderbolt.
“It was destiny that it wasn’t going to happen for us.
“On another day he could have slipped it into Brandon and it’s a different game but he didn’t. I was slightly agitated at that point but Tom Eaves didn’t mean to do it, he didn’t mean to give it away. You just have to get on with it.”
McBurnie’s opener had come just 10 minutes into the game and it was a difficult half for the Gills as they fought to stay in the tie.
“We knew what kind of game it would be,” said the manager.
“They are a passing side, they are fantastic, they are all top quality players, players we haven’t come across this year and it’s a good job really.
“I said to the boys they have to hold their hands up and say you have gone up against a top quality team, a team looking to get back in the Premier League and they have to be proud of what they have achieved.
“To get this far and with the effort they put in, they could have easily rolled over. At 3-1 and 4-1 they are still going, they are still trying and that is all you can ask.
“I wouldn’t expect any less of them. It is hard, we have all been out there as a player, you get to a certain point and think there is no way back but to keep going takes character.”