“We are still amongst it and there is belief amongst the group that we can play finals,” McVeigh said on Tuesday.
“If we win against Carlton [on Saturday] we are back in it.
“Anything can happen and there is strong character in this squad and we think we can do it.”
The Swans are currently in 11th position with six wins and nine losses while Carlton is seventh with eight wins and seven losses.
A win to the Swans this weekend would reduce the gap to four points but the Blues have a significant percentage advantage of more than 15 per cent.
McVeigh was a last-minute withdrawal against Essendon last weekend but expects to have a vital role this weekend matching the star-studded Carlton midfield.
“They have some very good players with obviously Brendan Fevola in fine form, Chris Judd, Marc Murphy and Bryce Gibbs in the middle, so it is important we shut them down,” he said.
As the Swans went through their warm-up in the match against Essendon on Saturday, McVeigh felt that his hamstring “just wasn’t right” and subsequently pulled out of the match allowing Canadian ruckman Mike Pyke to play his third game of the year.
The loss was a big blow for the Swans and a double whammy for McVeigh who missed out on the opportunity to play against his brother Mark.
“I trained well Thursday night but in the warm-up it didn’t feel right so I decided not to risk it,” McVeigh said. “We thought it was better to miss one week than one month.
“I felt it in the week before in the match against North and with the short week we thought it would be right but I could feel it not being totally free during the warm-up so it was better to be safe than sorry.”
McVeigh was not only disappointed with the loss, but family members had gathered to watch him and his elder brother Mark play against each other.
“It was shattering not playing last week against Mark,” he said. “It is frustrating not playing any game but with all the family there it made it harder.”
The 24-year-old was at a loss to explain the Swans’ poor performance on the weekend.
“We did look a bit tired,” he said.
“I don’t want to make excuses as we had a short week and we didn’t train much but the effort wasn’t there, which was the most disappointing aspect.”
McVeigh is coming to grips with his new role as the player being tagged instead of doing the tagging himself.
“I have been getting tagged this year, which is new to me and something I have to deal with,” he said.
“I wasn’t tagged at all last year but this year I have had a lot more attention and you have to learn to adapt as Ryan O’Keefe and Adam Goodes have been doing for years.”
Having missed out on the Swans' 2005 flag, McVeigh is very keen for more finals action.
“The whole reason you play is to make finals,” he said.
