Midfielder Shroot grabbed his seventh goal of the season to put Boro in front but it counted for nothing after Crawley hit back to win 2-1.
Next up is a trip to Griffin Park to face a Brentford side who moved joint-top of League One by beating Notts County.
But Shroot was in the team which secured a 1-0 win in west London last season and insists they can repeat the trick and keep their play-off bid on track.
"We need to carry on our away form at a side who are very much in and around the play-offs," Shroot told Boro's official website.
"We went there last year and I know we won and got a great result, but it's always a challenging place to go to.
"We've shown in this league that we can do things against those teams that are fighting for the play-offs and there's no reason why we can't have a fantastic week and put in a great performance."