The Jambos first-team coach has been asked to take care of team matters alongside player development manager Darren Murray after McGlynn was relieved of his post.
His first match in charge will be tomorrow's Gorgie clash with Motherwell but the former club captain was reluctant to speculate on whether he would still be picking the team by the time they run out at Hampden for the Scottish Communities League Cup final against St Mirren on March 17.
But should he decide to apply for the job, centre-back Webster insists he will be able to call upon the first-team members for a glowing reference.
He said: "That's a decision for the board to take but Lockey knows what it means to be at this football club as a player and a coach and the boys will be right behind him."
McGlynn was sacked after winning just eight of the 34 games he presided over as Hearts boss.
But Webster insists some of the flak that has gone the former manager's way is down to the players and their sub-standard displays.
He said: "Under the circumstances, of course it's been a difficult few days. It's never a nice situation to be in.
"In terms of results, we are where we are in the league but whether you are a player or a manager, results determine what's going to happen. For us to be in the situation we are is not acceptable.
"Do the players take a certain amount of responsibility for that? Yeah, and not just for the recent weeks, but from the start of the season.
"Individually and collectively, we need to take responsibility. The manager sets us up the way he wants and going out on the pitch we are more than capable of winning matches and it's not happened."
Former Raith Rovers boss McGlynn was unfortunate to take over the club while financial woes crippled the club and forced the exit of a number of high-earning regulars.
He was forced to promote a string of young players just to make up the numbers but was shown the door as Wednesday's 2-0 defeat to St Mirren saw them drop to second bottom of the Clydesdale Bank Premier League.
Now Webster feels the team's teenage crop must start showing they deserve their first-team slots.
He said: "The young players definitely have the talent, but you need to learn fast. We have a talented bunch coming through who are gaining a lot of first-team experience this season but when it boils down to it, you have got to win matches.
"We have played a lot of good football this season, but who wants to play good football and be sat 11th in the league."
Hearts have now sacked 10 managers since owner Vladimir Romanov seized control of the club in 2005. But Webster says only getting back to winning ways on a consistent basis will stop the managerial merry-go-round.
"From a footballer's point of view, stability comes with winning matches and pushing on up the league," he said. "But results haven't been anywhere near good enough and that's the players' responsibility. It has definitely got to be rectified."
Webster now hopes the fans who rallied to the club's cause late last year by raising £1.79million in a bid to stave off a winding-up order launched by HMRC over a £1.75million tax bill will continue to show faith in their team.
It was those cash problems that robbed McGlynn of so many the club's top players but the defender is hopeful of a brighter future.
He said: "The support we have had this year is hugely appreciated. But now more than most, we need everybody to stick together - the players, the coaches, the fans, everyone associated with the club, we all need to rally round.
"I'm sure in any managerial job, you would want a blank sheet to do as you please but circumstances dictate. We saw how serious it was at the tail end of last year so from that point of view, the survival of the club was paramount.
"Now we can bring stability to the club and pick up results on the pitch."