The Lilywhites lost 2-1 at home to UCL Division One side Lutterworth Athletic, also having a man sent off, to see any hopes of further progress ended.
And it left Rawlinson frustrated with the loss.
He said: "Ultimately we’re disappointed with being knocked out of the FA Vase.
"We’d been on a great run of form yet just when you think you’ve cracked it, football has a habit of teaching you that you haven’t.
"Fair play to Lutterworth, they came with good numbers in the squad and were a big side, and worked their socks off as you would against a higher level opponent.
“We didn’t respond to that. I think the game the previous week against Loughborough and then the match with Deeping where we had a small squad, eventually all caught up with us but that's taking nothing away from Lutterworth.
"We’re good when our attitude is right and our intensity levels are really high, but when they're not we can be left a bit wanting.
"Having said that, I was disappointed with the goal as we can defend that better, we perhaps scored an equaliser that shouldn’t have stood but then we conceded a minute after half-time after we’d changed shape to try and affect what they were doing.
"Then we’ve had a player sent off due to another individual error which threw all the plans and we were left huffing and puffing in the second-half.”
Skegness will now welcome mid-table Ashby Ivanhoe on Saturday as Rawlinson’s men aim to build on their current top six position.
He said: "Ashby will be a huge game. They’re new to the league and we know very little about other than them being a big and strong side and from what I’ve heard from teams that have played them.
"But ultimately we’re at home where we’ve only lost one league game and we want to keep that going as long as we can. We are six unbeaten in the league so need to get last Saturday out of our system and have a good go because if we want to be in and around the play-offs then we have to be winning our home games.
"The players know last weekend wasn’t good enough but I know them well enough and they’ll be smarting from that and will want to bounce back.”