Substitute Nicky Clark notched the winner as Rangers extended their unbeaten run in Scottish League One to 30 games with a 2-1 victory over Brechin City at Glebe Park.
Midfielder Fraser Aird opened the scoring for the champions in the 22nd minute when he capitalised on a mistake by City full-back Jonny Brown before Brechin striker Robert Thomson equalised four minutes into the second-half.
McCoist was pleased with the win but wants his side to fight to keep their shirt and not ease off as the season draws to a close.
"We have to perform at these places," McCoist told BT Sport 2.
"These performances in the league - they have to to keep hold of the jersey. We went about our business in the early stages of the game and we scored but we never had a top level of performance to be frank.
"We can keep going undefeated in the league which is a fantastic achievement at any level."
Despite the win, McCoist was frustrated when his side conceded a goal.
He said: "I was angry because I thought we should have stopped the cross initially. There was no-one within 10-15 yards of the cross and that's not good enough."
However, the Gers manager was satisfied overall, and reserved special praise for Clark, who scored after coming off the bench.
"I don't think the game was the easiest but we kept the momentum going and got another three points so we're very pleased," McCoist added.
"(The wind) definitely helped us and as crazy as it may seem I think he (Clark) would have been better starting the game because of the wind but he made a huge impact when he came on."