The Blues eventually came out on top 4-1 but Cole is struggling to prove to England coach Fabio Capello that he can play a part at the World Cup finals this summer.
The midfielder was sidelined for much of last year with knee ligament damage but Wilkins insists there is no problem with Cole.
“Joe wasn’t injured, it was just a tactical thing,” said Wilkins.
“We have a squad full of quality and therefore the manager will change things if he sees fit.
“We are very fortunate as far as that is concerned. I am not concerned about his form.
“When you have had a long lay-off like Joe, it really is a shock to the system. But it does take a bit of time to get back into your tip-top form.
“That will come with Joe. He is working extremely hard day-by-day, so we don’t see any problems there at all.”
However, Wilkins did admit Cardiff posed them plenty of problems in the opening half.
“It was tougher than we thought,” added Wilkins.
“We anticipated having a hard game. Cardiff played exceptionally well and gave us a lot of problems in the first half.
“But thankfully we managed to up the tempo in the second half and it became a tad easier for us. But we have got to give Cardiff credit as well. For an hour they gave us a tough old game.
“Our team was changed but we took quality out and quality came back in. It is the professionalism of our players that shines through.
“Some people might have thought this was going to be a bit of an easy game for us but those guys took it by the throat and pulled us through when we were not playing particularly well.
“I would include Frank Lampard in that as well. Full credit to those guys.”