Rafael Benitez hailed Peter Crouch's spectacular double but he knows he must solve defensive problems if Liverpool are to make any serious impact on the Champions League.
The Reds were 3-0 up thanks to Crouch's fine efforts and a header from Luis Garcia, but ended up hanging on to their precious three points to head Group C as Galatasaray swept back with two fine goals of their own from substitute Umit Karan.
It had Anfield in a state of nervous exhaustion by the end of a thrilling game in which they could easily have lost had former Blackburn striker Hakan Suker not missed two decent late chances.
Benitez described Crouch as 'amazing', with the big striker back in the front line after four games on the bench, hitting goals and form at just the right time to aid England's Euro 2008 qualifying campaign next month.
Crouch too, was delighted with his display and especially his second goal - a scissor-kick - telling Sky Sports: 'It was great. It's nice to get a goal like that. It was obviously a special one.
'That second one was my best for the club, you don't get too many of those. Most of the time they go over the stand and thankfully that one went in the corner and it's got us the win, so it's great.
'There are dangerous sides in the Champions League and if you step back and allow teams to come on to you it can become very difficult.'
Benitez revealed his relief at the end, with three points in the bag the hard way.
He said: 'It was a strange game, we started so well with lots of crosses, shots and goals.
'And we were well on top after just 20 minutes. But maybe we were thinking the job had been done, and then they started to cause us problems.
'The positives were the amazing second goal by Crouch. When you see him score a goal like that, a fantastic hooked volley, then you understand his quality.
'But Galatasaray started to move forward when they were three down with nothing to lose. They attacked with lots of players and we had trouble controlling the game after that.
'But we have taken three points, we are still unbeaten in the group and we are top as well. If we win our final two home games we should qualify.'
He added: 'I am normally calm and trying to analyse the game in the closing minutes, but we were under pressure and it was very difficult. But we aim to continue to look forward to the next match and we are grateful for the three points.'
Galatasaray coach Erik Gerets was angry with the mistakes that allowed Liverpool into a three goal-lead.
He said: 'We forgot to play football in that first half, we were too impressed by the surroundings and the team we were facing.
'If you play like that with stars in your eyes, then you end up losing. If we had played in the first half like we did in the second it would have been a different story.
'In that second period the team played so much better and attacked more and caused them many problems.
'We could easily have scored more, we missed some late chances to equalise. Now we are crying and unhappy and I am angry that too many players made too many mistakes at crucial times to give them goals.'