The Hammers were comfortable 3-0 winners in their first qualifying round, first leg tie on Thursday.
The Hammers took on Andorran side FC Lusitans on Thursday and ran out 3-0 winners courtesy of a Diafra Sakho double and an effort from defender James Tomkins.
That was the first leg of their first round tie as they seek to qualify for the Europa League group stages, and Burke says the squad can be pleased with how well they played considering their short preparation time for the game.
"I thought we played really well,” he told whufc.com.
“We came back early and only had ten days to prepare for the game but I thought we played well and could have had more goals. Every game is competitive and we treated it as a normal game. Yes, we were expected to win, but we prepared properly and got the win."
West Ham cannot afford a European distraction
A European run would naturally be widely welcomed by the Hammers fans, although they will be hoping it doesn’t prove to be a distraction to their Premier League campaign.
English teams have often struggled to marry both competitions in the past, with Everton last season suffering a noticeable decline in the league as a result of their Europa League excursions.
That is something Slaven Bilic’s side cannot afford, however, with Premier League football a necessity for when they move into the Olympic Stadium ahead of the 2016/17 campaign.