Manager Josh Dixon praised his side’s fighting spirit after the Red Badgers took the game into extra-time, levelling at the death last night.
“We were 2-1 up and they scored with the last kick of the game,” the manager said.
“To concede in the 93rd minute like that - the ref blew after the ball hit the net - the lads were down.
“But they showed what we’re about. Our quality came though in the end and our fitness showed as we scored two late goals.”
Zak Adams and Marshal Keenan appeared to have won the contest for the Swifts in normal time, but Jordan Small made sure of victory with two goals in the additional 30 minutes.
Kieran Knight netted twice for East Midlands Counties League Eastwood, who impressed Dixon.
“They’re a good side, doing well in their league,” he added.
“They’ve got two very good strikers, but our heavy, wet pitch definitely suited our style of play.
“It is what it is. You can only prepare the team as best you can for each game.”
Lutterworth will now face either UCL Premier rivals Leicester Nirvana or Hellenic League Premier Division outfit Westfields in round three, the sides yet to meet following two postponements.
“I’d rather play Leicester Nirvana,” Dixon confessed.
“We know about Westfields as we played them in the FA Cup. We went there and won 3-2.
“But they’re a good side, one of the best we’ve faced this season.
“I’d rather play Leicester. It’s less travelling and a good chance to get a good crowd.”