Lambert had nothing but praise for his side despite United's fine comeback.
Lambert said: "I am proud. I thought they were outstanding. I couldn't ask for any more. But that's why Manchester United are a top side. They do it week in, week out.
"I am really proud with what they have given me. I think we have been playing well for a couple of weeks, and hopefully the confidence will be there in abundance after that.
"The Premier League is really tough. They are a young side but they are playing really well at the minute.
"They kept on going. I couldn't fault them for the way the lads played and kept going. The crowd are your gauge. I am absolutely gutted to lose because they gave me everything they had."