The defender has also predicted bright futures for youngsters Reece Burke and Reece Oxford.
The Hammers are heading to Romania on Thursday for their second leg against Astra Giurgiu, after they surrendered a two-goal lead in their first leg tie at Upton Park.
That slip up came after James Collins saw red, their third sending off in as many rounds after Diafra Sakho and James Tomkins were also both sent off in the previous rounds.
Cresswell though, says they will try their hardest to progress believing the Collins red card ultimately changed the first leg.
"It's not going to be easy going away to Romania and we've got Arsenal on the Sunday as well,” he told whufc.com.
“We want to go as far as we can in the competition and we're going to try to do that. We were dominant in the first half but the game changed when James Collins got sent off. I still thought we had to be stronger to see it out.”
Bright future for youngsters
The defender also believes that youngsters Reece Burke and Reece Oxford have bright futures at the club.
The duo, as well as several other youngsters, have enjoyed increased playing time in this pre-season so far, with both having starred in both their Europa League qualifying round ties and regular pre-season friendlies.
And Cresswell says that the increased number of games has been a perfect opportunity for the youngsters in particular to show what they have to offer the new manager ahead of the new season.
“It's been a hectic schedule but it's been a good opportunity for the youngsters to show the Gaffer what they can do,” he added.
"We've had Saturday-Tuesday-Thursday over the last few weeks and the likes of Reece Oxford and Reece Burke have a bright future in front of them."