A superb strike from Leon Osman after 32 minutes and a breakaway effort from Nikica Jelavic in injury time secured a win that provided a stark contrast to last week's debacle.
Gibson said: "I think we needed to do that after the performance last week, but I think we have been great all season.
"Last week was a bad week for us but we have bounced back and showed what kind of a team we really are.
"We all knew as a team that wasn't Everton last week. We had an off-day.
"But we showed everyone what we can do, even going down to 10 men I think we still deserved the three points."