England forward Walcott came off the bench at Brighton to score a deflected goal with five minutes left which sunk the Championship side 3-2.
Arsenal will now head into Wednesday's home Premier League clash against Liverpool on the back of two confidence-boosting victories last week after they also destroyed West Ham 5-1.
Walcott feels these two results show Wenger's men can finish what has been a testing campaign on a high.
"I am very confident in the team, this team just needs to realise how good we actually are and not read into too many bad thoughts," said Walcott.
"We have a very good team, very young and great on the eye at times.
"We can be cold at times as well, but we are starting to learn and we are starting to get back to our best."
You can only watch the best Barclays Premier League coverage here on Sky Sports. Watch Arsenal v Liverpool exclusively live on Sky Sports HD2, 3D and Sky Go from 7.00pm on Wednesday 30th January. Click here for more details