Mercedes finished second and third at Barcelona's Circuit de Catalunya with seven times Formula 1 world champion Lewis Hamilton and George Russell securing the team's first double podium of the campaign.
Shovlin said in a team debrief that an upgrade package and the track characteristics helped Mercedes in Spain but Montreal was a very different circuit.
"There are more low-speed corners, quite a lot of straight-line full throttle and we would expect more of a challenge there," he said.
"We are not thinking that we are going in nipping at the heels of Red Bull.
"We are going in there prepared for a battle with Ferrari, Aston Martin and maybe even Alpine."
Champions Red Bull have won all seven races so far this season, with championship leader Max Verstappen taking five victories and Mexican teammate Sergio Perez his closest title rival with two.
Aston Martin are third overall, ahead of Ferrari and Renault-owned Alpine.
Shovlin noted that the difference between qualifying in second place and 10th on the grid came down to only a few tenths of a second.
"We are looking forward to more exciting racing but certainly we are aware that Canada is likely to be a bigger challenge than the Sunday we just had in Barcelona," he added.
Verstappen won from pole in Canada last year with Hamilton third, behind Ferrari's Carlos Sainz. Russell was fourth.
Hamilton took the first win of his Formula 1 career in Canada in 2007 with McLaren and has won that race seven times in total - a record he shares with Ferrari great Michael Schumacher.
