Welsh hopes of reaching the finals in Ukraine and Poland are in tatters after defeat in their opening Group G qualifier in Montenegro was followed by another loss to Bulgaria on Friday.
Collins accepts the odds of coming through a group that also includes England are already long but he is not prepared to give up just yet.
Wales face Switzerland in Basle on Tuesday needing an unlikely win in the second and final match of Brian Flynn's spell as caretaker manager to resurrect their slender chances.
Collins, 27, said: "Obviously it's going to be very difficult now to get to even second place.
"You can't expect to lose your first two games and qualify, so everyone has got to up their performance, starting with me as one of the oldest guys in the squad.
"Brian is obviously disappointed, he's come in for the two games and he wanted to do well, as we all do.
"Coming off the back off a defeat everyone is going to be disappointed for a day or so, but you have to lift yourself for the next game.
"We go into every game wanting to win, so there's no difference on Tuesday night.
"Obviously it's going to be tough over there, but that's what we've got to look to do."
Collins, with 36 caps, is now the most experienced member of Flynn's squad.
That mantle was held by Sam Ricketts (41 caps) on Friday but the Bolton defender is now suspended after collecting his second booking of the competition.
The sending off of Chris Gunter has robbed Flynn of another experienced defender while key midfielder Joe Ledley has returned home to be with his expectant partner.
With young striker Hal Robson-Kanu also pulling out injured and Joe Allen and Ched Evans unable to rejoin the squad due to hamstring problems, Flynn has been forced to draft in extra bodies.
Bournemouth defender Rhoys Wiggins and Swansea midfielders Shaun MacDonald - who is on loan at Yeovil - and Jazz Richards were added to the party which flew to Basle on Sunday night.
The task facing Wales is a daunting one but the Swiss are in a similar situation having also lost two from two and Collins retains optimism.
He said: "There are some disappointed lads about, they are young boys and some of them haven't been involved before so we have to try and lift ourselves for Tuesday.
"It shouldn't be hard to lift anyone because we are playing for Wales.
"You can't rule it [qualification] out until it's impossible but it's certainly going to be tough."
Source: Team Talk