Now they will face another test of their resolve against on-song Arsenal who demolished AZ Alkmaar in the Champions League on Wednesday night.
Kightly said: "Villa and Everton, for instance, are big sides who finished in the top six last season and we drew with them.
"You need to win games, we need to start getting three points, but we can build on the confidence from those games and being unbeaten in three matches.
"Everyone knows the Premier League is full of quality players but we have got a good set of lads here and a good staff and a good manager and we feel we can compete.
"Also, when we're the underdogs, it suits us and I think we can surprise a few people."
Kightly is happy to be back playing after injury problems and looking to make his mark in the top flight.
He said: "When you are not playing, it is terrible and so frustrating. I had played in 40-odd games last season to get into the Premier League.
"Then, once you are there, you find you can't taste what it is like, what it is all about, which was a really big blow for myself.
"It was really tough but I am pleased to be back and, the more minutes and games I play, I am sure the stronger and better I'll get."