Their next assignment is at Blackpool's Bloomfield Road on Tuesday, when they could move five points clear, but United have won only two of their 10 away matches so far.
"We've got to start winning games away from home," Phelan told BBC Sport. "We'll be on our toes [against Blackpool], we know what they're capable of."
We have some tough games ahead, but hopefully the players can grasp the nettle
United boss Sir Alex Ferguson
Giggs - who says he hopes to tie up another season's contract at United soon - insisted they must keep their feet on the ground and simply "keep winning" in order to keep title rivals such as Arsenal and Manchester City at bay.
When asked if they were easing away, he said: "No. There's a lot of tough games to come.
"You can never tell this season, it's been one of those years where everybody's been beating each other. So we'll just concentrate on our job, and hopefully the other teams will fall away."
Manager Sir Alex Ferguson welcomed Berbatov's third hat-trick of the season, while adding that he now hopes Wayne Rooney can enjoy a touch of luck in front of goal.
"We hope the goals are going to come for Wayne," he said. "He is working his socks off.
"He produced some great football, and his control from Edwin van der Sar's kick for the fourth goal was fantastic.
"[But] it was a marvellous performance from Dimitar. He could have scored more. We were a bit wasteful with our finishing at times, but you can't complain at the performance.
"[And] it certainly helps the goal difference, there is no question about that.
"We have some tough games ahead but hopefully the players can grasp the nettle. We have some experience. We have the squad. Hopefully we can manage all the games we have ahead."
Loss sets Blues back a mile - McLeish
Ferguson described Michael Carrick's ankle as "sore" after he was taken off in the first half, while the manager confirmed he will check on the state of Rio Ferdinand's groin injury on Monday before deciding whether to risk the England captain at Blackpool.
Birmingham boss Alex McLeish said the heavy defeat was not the ideal way to prepare for Wednesday's Carling Cup semi-final decider with West Ham.
"To lose a goal to a set-piece in the first minute was criminal," he said.
"We had a spell after that when we started to get in their final third, but to concede just before half-time was verging on the amateur."
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