The former England captain was discharged from hospital and returned to the team hotel in Auckland after undergoing surgery to have a plate and five screws inserted into his ankle.
Dallaglio dislocated his right ankle, broke his fibia and damaged ligaments when he slid into a tackle and was caught awkwardly under a pile of bodies in the first half of the Lions' 34-20 victory over the Bay of Plenty on Saturday.
Dallaglio will return home in about a fortnight, once the stitches have been removed from his leg, but believes the Lions can be victorious in New Zealand for only the second time ever.
"We can win the Test series against the All Blacks and this isn't about any one player," said Dallaglio.
"The guys have the firepower to achieve a series win. I believe we showed enough in the first game to suggest we are going to have an exciting tour.
"New Zealanders will have seen enough to realise this is going to be a Test series that will go all the way to the wire.
"Whether I am there or not is irrelevant because they will be in for a tough time.
"We have so many match-winners across the team - with Jason Robinson and Gareth Thomas still to arrive - and that's why it is so frustrating because I realise we have a chance of being very successful and I wanted to be part of that.
"England won here after 30 years of trying in 2003 and that proved it is possible and there aren't many bigger things in rugby than to be remembered as part of a Lions tour that won a series in New Zealand."
Dallaglio's experience and rare leadership qualities - not to mention the prime form he has been in - made him a central figure to the Lions' hopes of glory in New Zealand.
But Dallaglio predicted there will be others, perhaps surprisingly, who will grow as the tour unfolds.
"I am very disappointed that I cannot take any further part in the tour because I felt that I had a lot to offer," he added.
"I wanted to be part of achieving something very special over here and I believe the resolve of the team will be strengthened by what has happened.
"There are a number of players who will now have to step up in terms of leadership but we do have that kind of quality in the squad.
"Players will rise to the challenge and that's the beauty of this kind of tour, players relish the chance to put themselves forward.
"Players will come to the fore in, at times, the most peculiar of situations.
"Simon Easterby has come out here after a fantastic Six Nations and has a really good opportunity."
Despite all the trauma of having his tour ended by injury, Dallaglio made sure his number eight jersey was left on the peg of his Bay of Plenty opposite number Colin Bourke, who vowed never to wash it.