The Red Devils nabbed a 1-0 victory thanks to Marouane Fellaini's injury time strike.
Manager Jose Mourinho recently criticised his players for lacking heart, but Shaw says that wasn't the case in last night's encounter.
"It might not have looked like we did everything possible to win, but in the changing room we really wanted to win this game," Shaw told RTÉ Sport.
"Sometimes when you miss as many chances as we did tonight, it feels like we have been here before. The good thing was we didn't give in, we carried on going. Thankfully for Felle [Fellaini] we got the goal and qualified.
"We didn't create through the whole game, but we can get better as a team. This win could be the start of a push up the table and the next round of the Champions League."