The midfielder has signed a four-and-a-half year contract, which was announced just before Villa’s 2-1 FA Cup win over Bournemouth on Sunday.
Delph, who missed the game with an Achilles injury, was due to be out of contract at the end of the season and had been linked with Liverpool.
A breakthrough in talks was made earlier this month and Lambert admitted the 25-year-old would have been a huge loss.
“If you lose someone of that ilk it’s going to cost you a fortune to replace him,” he said. “It would take millions to replace him and we obviously can’t do it.
“I don’t know what his value is, ??15million? Whatever it is we’re not in a position to go and do things like that at this minute in time.
“It’s great for the club he is definitely staying, it makes common sense.
“It’s great for him as it puts everything to bed. I know from my own experience when you’re coming out of contract your head’s all over the place at times. He will be settled and he’ll be a big driving force behind this club in the next few years.”
And Lambert insisted Villa would not sell Delph should other clubs come in for him later.
“There’s no way that’s going to happen. With the way he handles himself, no way that’s going to happen,” he said.
Ron Vlaar’s future remains uncertain with his contract ticking down, but Lambert will continue to talk to his skipper.
He added: “He holds the ace card, as any player does when they are out of contract, but if we can keep talking let’s see. Everyone assumes Ron and Fabian were going to go, we’ve got Fabian and we just need to keep it going now.”
Carles Gil’s opener against Bournemouth – on his full debut – was just Villa’s second goal in 663 minutes and Andreas Weimann made it 2-1 with 19 minutes left before Callum Wilson’s stoppage-time consolation.
Eddie Howe’s Sky Bet Championship leaders impressed in the first half when Kieran Richardson cleared off the line from Shaun MacDonald and Eunan O’Kane was denied by Shay Given.
They are a point clear at the top and host Watford on Friday and Howe, who made eight changes, insisted his squad rotation did not have an impact on their fourth round defeat.
He said: “A lot is made of the changes we have made in the cups but there’s little difference from the established starting 11 and those who played, with different luck they would be starting. I had no problems bringing them in today.
“My team was picked a while ago, it was the team which beat Rotherham 5-1 and beat West Brom in the League Cup.
“We felt we were well in the game and we created the better opportunities. We had a good defensive structure and limited their chances and it took a moment of quality to break the deadlock and give Villa a lift.
“We went toe-to-toe with a Premier League club at their own ground.
“We did it pretty well but you could see the difference in quality with their goals and that is what we aspire to.”