Wilshere's superb left-footed finish from 20 yards finally shook off Swansea with four minutes left at the Emirates Stadium tonight as Arsenal won 1-0.
Belgian defender Vermaelen said: "He's a world-class midfielder and he showed again today [Wednesday], he played really well and was important for us.
"I'm really happy for him that he got the goal, and happy for the team."
Wilshere added on ESPN: "I don't know if I'll ever hit another one like that in my life, and it was a great set-up from Olivier (Giroud).
"It was important we got the win in 90 minutes, we'd created chances (before the goal) but we just couldn't put it in."
The competition represents arguably Arsenal's best chance of ending their long trophy drought this season, and Wilshere said: "We know what the FA Cup means in England.
"It's a great competition and we wanted to be in the next round, but we've got a tough game away to Brighton."
Swansea manager Michael Laudrup saluted his side's defensive efforts but admitted Arsenal were deserving winners.
"The first half was very even, they had a bit more of the ball but we were at the same level," he said.
"In the second half they were the better team, they deserved the win and good luck in the competition. They created chances and pushed us back, we defended great but we couldn't get out of there.
"It was nice to see Michel Vorm back at his best and we blocked a couple of big chances. They had one or two where you say 'How did they miss that?', and then they scored with a few minutes left. Last time it was us, this time it was them."
Gunners boss Arsene Wenger said he "always had faith" that his side would score, adding: "I always felt maybe one (chance) will go in. It was unbelievable that we didn't score (earlier). At least we scored before the end."
Wenger is delighted with Wilshere's return to full fitness, and with his versatility after the 21-year-old excelled in a more attacking role than usual.
"What is pleasing is that he's ahead of schedule," the Frenchman told ESPN. "Jack is completely back to his best and I would never have believed that would have happened as soon as January.
"He can play everywhere - he can defend and attack. He has got back his burst with the ball so I used him closer to the strikers and he was always dangerous."