Ashley Young's last-minute header rescued a point for United but Ferguson was not happy with the 3-3 draw.
He said: "I thought there was a carelessness about us throughout the game. The attacking part was very good at times - we played some very good football, particularly in the first half.
"But there was a carelessness about us and really, they could have scored three goals in the first half.
"I suppose in many ways, it is 'welcome to European football' because they were very lax for parts of the game."
He added: "We were careless. It's a wake-up call in many ways. A lack of concentration saw us give the game away really, but we rescued it."
United had appeared to be cruising through two goals in 80 seconds from Danny Welbeck but the Swiss side, who had missed some clear chances in the first half, stunned Old Trafford to go 3-2 up.
Two goals from Alex Frei, one from the penalty spot, and one from his namesake Fabian Frei, saw United come close to their first home defeat for 17 months.
Ferguson insisted Italian referee Paolo Tagliavento had been wrong to award a penalty against Antonia Valencia for a foul on Marco Streller.
He said: "We are disappointed with the penalty decision - I don't think it was ever a penalty kick, and a poor decision I felt.
"But it turned out to be a fantastic game with a great end in terms of excitement."
Ferguson said his defence still should have had enough experience to cope with Basle even with 19-year-old Phil Jones in central defence but admitted they are suffering from inconsistency.
"There is still enough quality in the back positions - Evra and Ferdinand are very experienced. But you always like to have a back four playing consistently and we don't have that at the moment.
"It is not a problem for us because of the quality we have in the forward positions guarantees us goals, and we really should have put that to bed tonight in the first half.
"We played with too many forward on the pitch tonight, far too many. I think that is possibly because we were playing a team like Basle, who in the players' minds, although we prepared properly, are a team where they can do that.
"In doing that, they left so many gaps in the back four and really if everybody had concentrated on the defensive part, I don't think we would have had so many problems."
Ferguson did praise Welbeck's contribution, saying the 20-year-old "did very well" in the first half but had tired in the second.
Basle coach Thorsten Fink - who was a player for Bayern Munich when they were beaten by United in the 1999 Champions League final - said: "It was a great result for us - I don't imagine many teams go two goals down here and then turn the game around. It was a great achievement.
"It was a great game for the fans, I think we were rather nervous in the first half but we settled down after the break and were able to take some chances.
"We deserved at least to draw and as a coach it feels good to come to a club like Manchester United and get such a result.
"The final in 1999 was more of a negative experience and I'm glad my team is able to celebrate tonight."