A first half goal from Jack Phillips want enough for the Oak as they were knocked out at the first hurdle.
Despite the result Foster held his head high at the performance of his players.
He added: “We gave our everything in the Vase it just wasn’t our day. Best of luck to Redhill in the next round who took their chances.
“The players are still battling as hard as ever. As the weather worsens and pitches worsen, we will have to adapt our game.”
The game started evenly, with both sides vying to claim a foothold in the tough conditions.
The visitors took the lead on 15 minutes as Jon Trotter rose highest from a Matt McKenzie long throw to give the Lobsters the lead,
Craig Anderson had a chance to equalise for the Oak but could only see his shot go wide of the Redhill upright.
The Lobsters then had a chance to make it two after Aaron Stenning spilled a tame shot but recovered well to save the follow up to keep the Redhill lead at just one.
The game was even on 41 minutes as Phillips powered home a left footed strike after a goal-mouth scramble after the visitors failed to deal with a corner.
Straight after the half-time break Redhill almost regained the lead but could only see their headed effort fall straight into Stenning’s hands.
Mile Oak then had a chance themselves to score but Joe Hall’s strike went wide of the posts.
The visitors took the lead on 60 minutes after some good play from Evan Lopes down the right allowed him to maraud into the box and pulling it back for Fred Hill to tap home.
Mile Oak seemed to come alive after the goal as they piled the pressure on and had several chances from corners to bring it level but Redhill stood firm.
Anderson then came close to evening the scores but his first time effort deflected agonisingly onto the post and out.
On the brink of stoppage time it should have been 2-2 but Anderson shot wide of the post after some excellent play by David Marsh on the right as it finished 2-1.
The Oak host AFC Varndeanians on Saturday and Foster is expecting a tough game.
He added: “Varndeanians are flying high and will be an incredibly tough test for us, as they will be for all teams this year.”
Mile Oak: A Stenning, H Dunk, Phillips, Hall, Early, Austin-Slade (Benn), Foster, Marsh, Rudwick, Marriott (Dine), Anderson
Unused: R Dunk, J Stenning, Rose, Gould