The Scot blasted his side's defending after successive Old Trafford defeats in Europe and labels Rio Ferdinand a key player to come in for the second leg in Spain next week
A Wayne Rooney double and a heroic performance from David de Gea kept United in the tie but Sir Alex conceded that his defence had a poor night.
"We were well beaten, Bilbao were the better team," Ferguson told Channel 5.
"I thought our defending really wasn’t very good tonight, that kept us on the back foot all the time."
However, the 70-year-old insists is side have hope for the second leg, despite the Basque side notching three away goals.
Ferguson also singled out Rio Ferdinand as the man to shore up the Red Devils' defence but says he will only play the 33-year-old if it does not impact on United's Premier League ambitions.
He continued: "Our attacking play was very good at times. It was a really open match, an entertaining match. On the night Bilbao were the better team.
"We can win the game [at Bilbao next week], I don’t think there’s any question about that, we showed tonight that we can make chances against them.
"Obviously we’re going to have to defend better, that goes without saying.
"I need to find a way of bringing Ferdinand in without disrupting our league programme because Ferdinand’s an important figure in terms of experience."
Bilbao's third goal was scored in controversial circumstances, with the referee awarding the Spaniards a free-kick after Patrice Evra's boot came loose, and Ferguson was baffled by the decision.
"The third goal, I don’t know how to describe it," he explained.
"The issue of him not having a boot on, they said you’re not allowed to do that."