The Foxes suffered a surprise 4-2 defeat to Newcastle on Friday to dent their top-four hopes.
Callum Wilson’s brace added to goals from Joe Willock and Paul Dummett – his first in over five years – as the hosts fell apart.
It raised memories of last season’s late collapse, when the Foxes missed out on the Champions League places on the final day.
But with Chelsea and West Ham breathing down their necks, Albrighton insisted third-placed Leicester will regroup.
“Mistakes have cost us, mistakes that we’re not normally used to seeing,” said the winger, whose side face Manchester United, Chelsea and Tottenham in their final Premier League games.
“It’s frustrating, it’s disappointing. We’ve got to pick ourselves up.
“We’ve got three games left and we’re in a great position. We can’t let one silly performance, one silly result, stop us.”
The Foxes never looked comfortable after losing Jonny Evans in the warm-up to his persistent heel injury.
Albrighton, who along with Kelechi Iheanacho scored late on, replaced him at the last minute and the winger admitted it disrupted the hosts.
“Obviously, everyone can look at that change so late on, and yes, it’s not ideal,” he told LCFC TV.
“We worked on the training pitch with Jonny in the team and that personnel but from my point of view, I always make sure I’m ready if I have to step in, whether it’s before a game, five minutes into a game, or five minutes from the end.”
Victory put Newcastle on the brink of safety and their Premier League status will be confirmed if Fulham fail to beat Burnley on Monday.
Bruce hails counter-attack
Boss Steve Bruce labelled it as the Magpies’ best performance under him and was delighted with the response from the 2-0 defeat to Arsenal.
He said: “It doesn’t help when we concede a goal like we did against Arsenal. Although it’s been a bit different with no supporters, we took a backwards step too early.
“The energy and drive of the team was evident from the start (against Leicester), we had an early chance and got on the front foot and what a difference that makes.
“Considering who we were playing against, the magnitude of the game and how we went about it, that first half in particular I really enjoyed watching us play. Playing on the counter-attack worked extremely well.”