England international Welbeck had not kicked a ball for the Gunners in 10 months but returned with an instant impact on Sunday, glancing home an stoppage-time winner to beat the Premier League leaders.
Leicester had taken the lead through a Jamie Vardy penalty, only to see Danny Simpson sent off early in the second half for two bookable offences.
His dismissal set up an intriguing finish and, after Theo Walcott levelled having come off the bench, Welbeck followed him onto the pitch and flicked home Mesut Ozil’s late free-kick to move Arsenal to within two points of top spot.
Welbeck underwent surgery on a knee injury in September having not played since April but has now returned at a vital time for Arsene Wenger’s side — with FA Cup and Champions League fixtures coming up in the next week.
And Mertesacker believes the former Manchester United man, and other players returning from long-term injuries such as Santi Cazorla and Jack Wilshere, will all have a role in helping the side lift silverware this campaign.
“Yes, he does,” the German World Cup winner replied when asked if Welbeck now has a big part to play.
“We need players coming back. We had a lot of long-term injuries and that’s what gave us a bit of struggle in January because we played in December and then January with almost the same team.
“Players who gave us great energy stepped in but now we need other players to come back.
“We are happy to have Danny back and a few others are not far.
“We need all our players. In the end, that makes the difference. There’s more coming from other players as well.”
Mertesacker also praised Welbeck for proving doubters wrong as he hit one of Arsenal’s most crucial goals of the season to date.
When asked what the players had said to Welbeck, Mertesacker replied: “A hug and a well done says it all.
“For him, to go through a bad period, an injured period where he kept believing in himself when everyone maybe doubts him, it was a great chance for him to come in and show he is ready.
“He was always integrated in the team but when you feature on the pitch and give the team such a great goal and energy, it gives himself a big lift.”
Arsenal now face Hull in the FA Cup and Barcelona in the Champions League before they return to league action against Manchester United on February 28.
And Mertesacker feels the manner of the victory over Leicester, who had only lost twice in the league heading into the game at the Emirates Stadium, could have a more lingering effect on morale.
“When the referee blew the whistle for the final time it was a big relief honestly,” he added.
“The energy that created was absolutely fantastic, for us, for the fans, for everyone at this club. Everyone is very focused now but relieved as well.”
While Mertesacker wants the win to have a lasting impact on the Arsenal dressing room, Leicester goalkeeper Kasper Schmeichel insists the Foxes will dust themselves off and get back to it after a week off.
He said: “Why shouldn’t we (bounce back)? It is a loss, we move on and we will have the same attitude.
“We have only lost three games this season so we will not get bogged down by this in the same way we do not get too ahead of ourselves if we win.
“It is a loss and we will get on with it. It is a loss and it is not the end of the world.”