Former Burlington Jackdaws ace Beckett, who joined his home-town club on loan from Hull City last week, was handed his debut in the 0-0 draw against Stocksbridge last Saturday after only 30 minutes as Danny Earl went off with a hamstring injury.
Beckett had the chance to win it late on but shot wide, and Agnew admits he was gutted for the youngster.
Agnew said: “It was a good chance in front of goal, and you could tell Louis was upset after the game but I said to him don’t spend too much time worrying about as that is just how it goes for strikers.
Scarborough Athletic's home National League North campaign off to a winning start against Hereford
Breidyn Schaper sparkles with the bat as Scarborough CC experience mixed weekend
Folkton & Flixton CC net fifth YPLN Championship win in a row on the road at Easingwold
PHOTO FOCUS - 17 photos from Scarborough CC v Sessay CC by Simon Dobson
RETRO SPOTLIGHT: 15 nostalgic Scarborough photos from the Scarborough News sports archives
“I was desperate for him to score as there is nothing better than scoring for your home town club.
“He played out wide as one of three forwards for us Saturday but I think he could do a job up front too.
“Louis did very well against Stocksbridge, and got a great reception from the crowd when he was brought on.
“He made some good runs, showed some neat footwork and impressed me, he maybe needs to look a bit at his hold-up play but that will come with time as he is such a young lad.
“I have been keen on building this link between Hull City and Bridlington Town, and to get a local lad in as well is a big boost for the club.”
Agnew admitted his side were rusty on Saturday after a month on the sidelines.
He said: “We were not really at it in the first half Saturday, which was understandable with us having not played for a month.
“When we got in at the break I had a word with the lads and said we needed to improve. They reacted well to play better in the second period, but in the end only a couple of superb saves from keeper James Hitchcock kept it goalless so it may well end up being a good point earned against a side which had been in good form previously.
“We could well have nicked it though with Louis’ late chance.”
The match at fellow strugglers Frickley this Saturday is a huge game for the Seasiders, as they know a win would lift them clear of the drop-zone and ahead of their hosts.
Agnew said: “We now have eight games left and know that three wins can probably keep us up, so it is a massive six-pointer for us on Saturday against a side down there in the relegation zone with us.
“Danny Earl has a hamstring injury which will keep him out for two or three weeks, but otherwise we have a full squad to chose from.
“I will train twice this week and if I come through it okay I will take a place on the bench as with Danny out we need to have an extra attacking option in the squad with so much resting on this game.
“Frickley are a big, strong physical side and being able to bring me on to hold the ball up or flick it on late on could be handy.”